The document is calculating the probability of randomly selecting a 5-digit number greater than 65,000 where the numbers cannot be repeated. It does this in two steps: 1) It calculates there are 1,344 possible 5-digit numbers between 65,000 and 65,999. 2) It then calculates there are 9,075 possible numbers between 70,000 and 99,999. Adding these together gives a total of 10,416 possible numbers greater than 65,000. It then divides this by the total number of possible 5-digit numbers (90,000) to calculate the probability as 11.57%.

1. Probability By TN All of the calculations base on TI-84 Plus

2. What’s the probability if randomly selected 1 of the numbers which have 5 digit numbers, greater than 65000 , and the number cannot repeat ? ضطش

3. FIRST STEP …

4. Because we calculate from 65000 to 69000. So that it must has 1 choice. 6 5 0 0 0 1 At first, we need to know how many number from 65000 to 65999 and the numbers cannot be repeat.

5. Because we calculate from 65000 to 69000. So that it must has 1 choice. We have 4 number greater than 5, except 6 (1 st number).So that it must be 5-1=4 6 5 0 0 0 1 4 At first, we need to know how many number from 65000 to 65999 and the numbers cannot be repeat.

6. Because we calculate from 65000 to 69000. So that it must has 1 choice. We have 4 number greater than 5, except 6 (1 st number).So that it must be 5-1=4 6 5 0 0 0 1 4 8 We have 8 numbers to chose (except 2 letters before) At first, we need to know how many number from 65000 to 65999 and the numbers cannot be repeat.

7. Because we calculate from 65000 to 69000. So that it must has 1 choice. We have 4 number greater than 5, except 6 (1 st number).So that it must be 5-1=4 6 5 0 0 0 1 4 8 We have 8 numbers to chose (except 2 letters before) 7 We have 7 numbers to chose (except 3 letters before) At first, we need to know how many number from 65000 to 65999 and the numbers cannot be repeat.

8. Because we calculate from 65000 to 69000. So that it must has 1 choice. We have 4 number greater than 5, except 6 (1 st number).So that it must be 5-1=4 6 5 0 0 0 1 4 8 We have 8 numbers to chose (except 2 letters before) 7 We have 7 numbers to chose (except 3 letters before) 6 At first, we need to know how many number from 65000 to 65999 and the numbers cannot be repeat. We have 7 numbers to chose (except 3 letters before)

9. Because we calculate from 65000 to 69000. So that it must has 1 choice. We have 4 number greater than 5, except 6 (1 st number).So that it must be 5-1=4 6 5 0 0 0 1 4 8 We have 8 numbers to chose (except 2 letters before) 7 We have 7 numbers to chose (except 3 letters before) 6 x x x x Multiply it, we will have the total of number greater than 65000 and smaller than 69999 At first, we need to know how many number from 65000 to 65999 and the numbers cannot be repeat. We have 7 numbers to chose (except 3 letters before)

10. Because we calculate from 65000 to 69000. So that it must has 1 choice. We have 4 number greater than 5, except 6 (1 st number).So that it must be 5-1=4 6 5 0 0 0 1 4 8 We have 8 numbers to chose (except 2 letters before) 7 We have 7 numbers to chose (except 3 letters before) 6 x x x x Multiply it, we will have the total of number greater than 65000 and smaller than 69999 At first, we need to know how many number from 65000 to 65999 and the numbers cannot be repeat. 1 x 4 x 8 x 7 x 6 =1344 numbers We have 7 numbers to chose (except 3 letters before)

11. SECOND STEP

12. 7,8,9 at 1 st position can make the numbers greater than 7000 (the numbers after cannot be repeated => exclude 70000) 0 0 3 0 0 7 Then, we need to know how many number greater than 65999, from 70000 to 99999 and the numbers cannot be repeat.

13. 7,8,9 at 1 st position can make the numbers greater than 7000 (the numbers after cannot be repeated => exclude 70000) 0 0 3 0 0 7 Then, we need to know how many number greater than 65999, from 70000 to 99999 and the numbers cannot be repeat. 9 We have 9 numbers to chose (except 1 letters before)

14. 7,8,9 at 1 st position can make the numbers greater than 7000 (the numbers after cannot be repeated => exclude 70000) 0 0 3 0 0 7 Then, we need to know how many number greater than 65999, from 70000 to 99999 and the numbers cannot be repeat. 9 We have 9 numbers to chose (except 1 letters before) 8 We have 8 numbers to chose (except 2 letters before)

15. 7,8,9 at 1 st position can make the numbers greater than 7000 (the numbers after cannot be repeated => exclude 70000) 0 0 3 0 0 7 Then, we need to know how many number greater than 65999, from 70000 to 99999 and the numbers cannot be repeat. 9 We have 9 numbers to chose (except 1 letters before) 8 We have 8 numbers to chose (except 2 letters before) 7 We have7 numbers to chose (except 3 letters before)

16. 7,8,9 at 1 st position can make the numbers greater than 7000 (the numbers after cannot be repeated => exclude 70000) 0 0 3 0 0 7 Then, we need to know how many number greater than 65999, from 70000 to 99999 and the numbers cannot be repeat. 9 We have 9 numbers to chose (except 1 letters before) 8 We have 8 numbers to chose (except 2 letters before) 7 We have7 numbers to chose (except 3 letters before) 6 We have 6 numbers to chose (except 4 letters before)

17. 7,8,9 at 1 st position can make the numbers greater than 7000 (the numbers after cannot be repeated => exclude 70000) 0 0 3 0 0 7 Then, we need to know how many number greater than 65999, from 70000 to 99999 and the numbers cannot be repeat. 9 We have 9 numbers to chose (except 1 letters before) 8 We have 8 numbers to chose (except 2 letters before) 7 We have7 numbers to chose (except 3 letters before) 6 We have 6 numbers to chose (except 4 letters before) x x x x

18. 7,8,9 at 1 st position can make the numbers greater than 7000 (the numbers after cannot be repeated => exclude 70000) 0 0 3 0 0 7 Then, we need to know how many number greater than 65999, from 70000 to 99999 and the numbers cannot be repeat. 9 We have 9 numbers to chose (except 1 letters before) 8 We have 8 numbers to chose (except 2 letters before) 7 We have7 numbers to chose (except 3 letters before) 6 We have 6 numbers to chose (except 4 letters before) x x x x Multiply it, we will have the total of number greater than 65999 and smaller than 99999 3 x 9 x 8 x 7 x 6=9075 numbers

19. And now, we add it together to get the 5 digit number greater than 65000. 1344+9072=10416 numbers

20. To calculate the probability, we need to know how many number have 5 digit number

21. To calculate the probability, we need to know how many number have 5 digit number Exclude 0 because if 0 lay at 1 st position, it will make the number with 4 digit. 9

22. To calculate the probability, we need to know how many number have 5 digit number 9 Exclude 0 because if 0 lay at 1 st position, it will make the number with 4 digit. 10 10 10 10 The number can be 0 and repeated

23. To calculate the probability, we need to know how many number have 5 digit number x x x x 9 Exclude 0 because if 0 lay at 1 st position, it will make the number with 4 digit. 10 10 10 10 The number can be 0 and repeated = 90000 Multiply it, we will have the total number have 5 digit numbers

24. PROBABILITY IS 10416/90000 217/1875 (11.57%)