Question
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?
Answer: Option C
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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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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