P and c session 1

1. Alosies George
IIM Calcutta
alosies@gmail.com
+91- 9985-372-371
www.georgeprep.com
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Permutations and Combinations concept session 1

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Permutations and Combinations
Permutations Combinations
Grouping and
Miscellaneous

3. The principle of counting
Addition (Or)
 Example: selection of one number among
(1,2,3,...9) or one alphabet among
(a,b,c,d......,z)
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Multiplication (And)
• Example: selection of one number among
(1,2,3,...9) and one alphabet among
(a,b,c,d......,z)

4. Permutation vs Combination
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Permutation: Number of ways of selecting n
distinct things from r distinct things
Combinations: Number of ways of selecting n
distinct things from r distinct things

5. Permutations
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If each letter is to be used exactly once, In how many ways can the letters of the
word SOLDIER be
1. arranged
2. rearranged
3. arranged such that they begin with S
4. arranged such that they begin with S and end with R
5. arranged such that they neither begin with S nor end with R
6. arranged such that they don’t begin with S or end with R
7. arranged such that S and R are together
8. arranged such that S, O and R are together

6. Permutations
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If each letter is to be used exactly once, In how many ways can the letters of the
word SOLDIER be
9. arranged such that S, O and R are never together
10. arranged such that all the vowels are together
11. arranged such that no two vowels are together
12. arranged such that no two consonants are together
13. arranged such that they begin and end with vowels
14. arranged such that S comes before R
15. arranged such that S comes before O, O comes before D and D comes before R

7. Permutations – Dictionary Rank
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If each letter is to be used exactly once and all possible arrangements of the word MIXTURE are arranged
in dictionary order, what is the rank of the word MIXTURE?
How about ALLIGATION?

8. Permutations –where not all are different
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No of permutations of n things, taken all at a time, of which
P are of one kind,
q are of the second kind and
rest are different.
𝑛!
𝑝! 𝑞!

9. Permutations –where not all are different
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If the letters of the word CONSONANT are arranged, taking all at a time, find the number of
arrangements in which,
The three Ns are together.
The arrangement begins with 2 Os.

10. Permutations – where repetitions are allowed
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In how many ways can 6 prizes be distributed to 4 girls when each girl is eligible for all the prizes?
Number of permutations of n different things taken r at a time, where each may be repeated any
number of times = 𝑛 𝑟

11. Circular Permutations
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There are three boys and 4 girls in a class
In how many ways can they be seated around a circular table?
In how many ways can they be seated around a circular table, such that no two boys are together.?
In how many ways can they be seated around a circular table, such that no two girls are together?
Number of circular permutations of n objects is (n-1)!
If anti-clockwise and clockwise distributions are different, then
𝑛−1 !
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