Permutations & Combinations Mcqs


Q.  A group of 10 representatives is to be selected out of 12 seniors and 10 juniors. In how many different ways can the group be selected, if it should have 5 seniors and 5 juniors?

a. ¹²C₅ * 10
b. ¹²C₇ * 10
c. ¹²C₇ * ¹⁰C₅
d. 12 * ¹⁰C₅


ANSWER: See Answer
 
Here, five seniors out of 12 seniors can be selected in ¹²C₅ ways. Also, five juniors out of ten juniors can be selected ¹⁰C₅ ways. Hence the total number of different ways of selection = ¹²C₅ * ¹⁰C₅ = ¹²C₇ * ¹⁰C₅

= ¹²C₅ = ¹²C₇
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