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Quantitative Aptitude

Combination

There are 15 ...

Question

There are 15 juniors and 21 seniors in the Service Club. The club has to send four representatives to the State Conference.

(i) How many different ways are there to select a group of four students to attend the conference?

(ii) If the members of the club decide to send two juniors and two seniors, how many different groupings are possible?

A

(i): ³⁶C₄ , (ii): ¹⁵C₂×²¹C₂

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B

(i): ²¹C₄ , (ii): ¹⁴C₂×²³C₂

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C

(i): ¹⁵C₄ , (ii): ¹⁵C₂×²¹C₂

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D

(i): ³⁶C₄ , (ii): ¹⁴C₂×²¹C₂

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E

None of these

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Solution

The correct option is A
(i): ³⁶C₄ , (ii): ¹⁵C₂×²¹C₂

The number of ways of selecting a group of four students to attend the conference = $^{36} C_{4}$

The number of ways of selecting a group of four students such that the members of the club have two juniors and two seniors = $^{15} C_{2}$ $\times$ $^{21} C_{2}$

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