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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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