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# Applied 40S March 9, 2009

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More on the fundamental principle of counting, factorial notation, and permutations.

More on the fundamental principle of counting, factorial notation, and permutations.

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### Transcript

• 1. It's coming ... can you see it? Pi by ﬂickr user Gregory Bastien
• 2. Permutations of Non-Distinguishable Objects We're Non-Distinguishable! I can't tell the difference! My Lovely Twins
• 3. (a) How many different 4 digit numbers are there in which all the digits are different? (b) How many of these numbers are odd? (c) How many of these numbers are divisable by 5? HOMEWORK
• 4. (c) How many of these numbers are divisable by 5?
• 5. (a) How many 3-digit numbers can be formed if no digit is used more than twice in the same number? HOMEWORK (b) How many of these numbers are odd? (c) How many of these numbers are divisable by 5?
• 6. (c) How many of these numbers are divisable by 5?
• 7. In how many ways can 8 books be arranged on a shelf, if 3 particular books must be together? HOMEWORK
• 8. In how many ways can 5 people be seated in a straight line?
• 9. Factorial Notation When we want to multiply all the natural numbers from a particular number down to 1, we can use factorial notation to indicate this operation. The symbol quot;!quot; is used to indicate factorial. This notation can save us the trouble of writing a long list of numbers. For example: 6! means 6 x 5 x 4 x 3 x 2 x 1 = 720 On the calculator ... Press: [MATH] 4! = 4 x 3 x 2 x 1 = 24 [<] (Prb) [4] (!) 10! = 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 3 628 800 1! = 1 By deﬁnition 0! = 1
• 10. In how many ways can six students be seated in 8 vacant seats?
• 11. Permutations (the quot;Pickquot; Formula) A permutation is an ordered arrangement of objects. n is the number of objects On the calculator ... available to be arranged Press: [MATH] [<] (Prb) r is the number of objects [2] (nPr) that are being arranged. Examples: In how many ways can 5 people In how many ways can six be seated in a straight line? students be seated in 8 vacant seats?
• 12. (a) How many “words” of 4 different letters each can be made from the letters A, E, I, O, R, S, T? HOMEWORK (b) How many of these words begin with a vowel and end with a consonant? (c) In how many of these words do vowels and consonants alternate?
• 13. (a) How many numbers of 5 different digits each can be formed from HOMEWORK the digits 0, 1, 2, 3, 4, 5, 6? (b) How many of these numbers are even?
• 14. (a) In how many ways can 4 English books and 3 French books be HOMEWORK arranged in a row on a shelf? (b) In how many of these ways will the French books be together?