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# Organized Counting & Combinations

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What is the value of C(15,4) is:
a) 1 365
b) 36 036
c) 3 003
d) 32 760

The number of combinations of 9 items taken 4 at a time is:
a) C(4,9)
b) C(9,4)
c) P(9,4)
d) C(9,3)

For a Data Management quiz, the teacher will choose 11 questions from the 15 in a set of review exercises. How many different sets of questions could the teacher choose?
a) 32 760
b) 165
c) 3 003
d) 1 365

If all 14 people at a party shake hands with everyone else at the function, the total number of handshakes is:
a) 91
b) 28
c) 90
d) 16 384

In how many ways can a 12-member jury be chosen from a pool of 22 citizens? a) 2 640
b) 646 646
c) 3 628 800
d) 479 001 600

https://brainmass.com/math/combinatorics/organized-counting-combinations-345525

#### Solution Preview

C(N,M) is defined as the quotient N!/(M!(N-M)!) The trick to calculate it is to wite down the product taht makes the factorial in the numerator and the products in the denominator and cancel as many factors as possible. For example, for

C(15,4) = 15!/(4!(15-4)!) = (2 3 4 5 6 7 8 9 10 11 12 13 14 15)/((2 3 4)(2 3 4 5 6 7 8 9 10 11))
We ...

#### Solution Summary

Organized Counting & Combinations are shown.

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## Organized Counting/Combinations

How many subsets of {1, 1, 2, 2, 2, 3, 4, 4, 5} will contain a 2?

A group organizing Smith College's alumni reunion includes 6 current students, 8 current staff members and 11 alumni. Two individuals from each category will work on the publicity committee. Use combinations to determine the number of different publicity committees the group could form.

A gardener bought five geraniums, three rose bushes and four evergreen bushes from a nursery that had fourteen geraniums, twelve rose bushes and only five evergreen bushes. How many choices did the gardener have?

A 15-passenger shuttle bus takes athletes between vanues at the Canada Summer Games. If 32 athletes need to get to the track and field stadium, in how many ways can passengers be chosen for:

a) the bus's first trip?

b) the bus's second trip?

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