SOLUTION: A student is to answer 8 out of 10 questions in an examination. How many choices have the student

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Question 1092066: A student is to answer 8 out of 10 questions in an examination. How many choices have the student
Answer by math_helper(2461) About Me  (Show Source):
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The student has C(10,8) ("10 choose 8") also written 10C8 (usually the 10 and 8 are subscripted) or +%28matrix%282%2C1%2C%2210%22%2C+%228%22%29%29+
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The formula is:
nCr = n! / ((n-r)!*r!)
where n! = n*(n-1)*(n-2)*…*3*2*1
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You will usually get a lot of cancellation in finding C(n,r) as the n! / r! part (or n! / (n-r)! part) cancels a lot of the multiplications (the closer r is to n or the closer n-r is to n, the MORE cancellations you will get). To see this in this problem, note that 10! = 10*9*(8!) so we can write:

10C8 = 10!/((10-8)!8!) = (10*9 * 8!)/(2! * 8!) <—— the 8!'s cancel
= 10*9/2
= +highlight%2845%29+