A team of 12 men is to be formed out of n persons. Then the number of times number of times 3 men ‘C’ ‘D’ and ‘E’ are together is ?
(a) nC12
(b) n-1C11
(c) n-2C10
(d) n-2C10
The correct answer for Q116 is
(d) n-2C10
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Put C,D and E as one unit
∴ Total people to be selected = 10 = 9 ppl + one group of 3
Similarly total no ppl= n-3+1 = n-(C,D,E) + a group of 3 ppl [Note:Here 3 ppl are replaced by one group of 3 ppl ∴ there are counted as one and not 3]
∴
Selection:n-3+1 C10 = n-2C10
∴ Total people to be selected = 10 = 9 ppl + one group of 3
Similarly total no ppl= n-3+1 = n-(C,D,E) + a group of 3 ppl [Note:Here 3 ppl are replaced by one group of 3 ppl ∴ there are counted as one and not 3]
∴
Selection:n-3+1 C10 = n-2C10
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