The retirement plan for a company allows employees to invest in 10 different mutual funds. Six of the 10 funds grew by at least 10% over the last year. If Sam randomly selected 4 of the 10 funds, what is the probability T that 3 of Sam’s 4 funds grew by at least 10% over last year?  Pick one.
A) 6C3 / 10C4  B) 6C3 * 4C1 / 10C4  C) 6C3 * 4C1 / 10P4  D) 6P3 * 4P1 / 10C4  E) 6P3 * 4P1 / 10P4
Look at the answers. B is the only answer choice that uses only combination formulas and takes into account all the factors.   We know this is a combination, not a permutation. This rules out choices C, DE.   A clearly isn't the answer because T= 6C3 only accounts for 3 of the funds he chose. 10C4, the denominator, is correct, so the numerator must be wrong.   6C3 * 4C1 / 10C4 it is.
<result>B</result>
The retirement plan for a company allows employees to invest in 10 different mutual funds. Six of the 10 funds grew by at least 10% over the last year. If Sam randomly selected 4 of the 10 funds, what is the probability T that 3 of Sam’s 4 funds grew by at least 10% over last year?