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Unit 13: Combinations

7. John has got 1 dollar, with which he can buy green, red and yellow candies. Each candy Notes
costs 50 cents. John will spend all the money he has on candies. How many different
combinations of green, red and yellow candies can he buy?
8. The board of directors of a corporation comprises 10 members. An executive board, formed
by 4 directors, needs to be elected. How many possible ways are there to form the executive
board?
9. Jose has 9 friends that he wants to invite to dinner but he can only invite six of them at one
time. Out of the nine friends many different groups can he invite?
10. Over the weekend, your family is going on vacation, and your mom is letting you bring
your favorite video game console as well as five of your games. How many ways can you
choose the five games if you have 12 games in all?

Answers: Self Assessment

1. combination 2. selection

! n
3. formula 4. n C 
r
(n r )! !

r
5. order 6. n-p C
r-p
7. n-p C 8. binomial expansion
r
9. distinct 10. C(n, r)
11. Multinomial 12. same

! n
13. 14. sieve
r
r
r ! !... !
1 2 m
n
15. N – S + S – S +… +(–1) S +… +(–1) S
k
1 2 3 k n
13.8 Further Readings

Books Giri&Banerjee, Introduction to Business Mathematics, Academic Publishers.
Jacobus Hendricks van Lint, A Course in Combinatorics, Cambridge University
Press.
Marshall Hall, Combinatorial Theory, John Wiley & Sons.

Online links www.mathwarehouse.com/probability/combination.php

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