SOLUTION: 1. Evaluate 5C3 × 10C2 2. Solve for n, nP6 = nP4 × 4P2

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Question 1202426: 1. Evaluate 5C3 × 10C2
2. Solve for n, nP6 = nP4 × 4P2
Answer by greenestamps(13215) About Me  (Show Source):
You can put this solution on YOUR website!


1. This is simply a calculation; there should be no need for you to ask us to do it for you....



2. nP6 = nP4 × 4P2


%28n-4%29%28n-5%29=12

This can be solved by inspection. (n-5) and (n-4) are two consecutive integers whose product is 12, so they are 3 and 4; that makes n = 8.

ANSWER: n = 8

Using formal algebra....

%28n-4%29%28n-5%29=12
n%5E2-9n%2B20=12
n%5E2-9n%2B8=0
%28n-8%29%28n-1%29=0
n=8 or n=1

Reject the solution n=1, because the expressions 1P6 and 1P4 are undefined.

ANSWER (again): n=8