To fill 12 vacancies there are 25 candidates of which 5 are from scheduled castes. If 3 of the vacancies are reserved for scheduled caste candidates rest are open to all, find the number of ways is which the selection can be made .
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Q)
True-or-False:To fill 12 vacancies there are 25 candidates of which 5 are from scheduled castes.If 3 of the vacancies are reserved for scheduled caste candidates while the rest are open to all,the number of ways in which the selection can be made is 5C3×20C95C3×20C9
(A)True(B)False(A)True(B)False
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A)
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C(n,r)=n!r!(n−r)!C(n,r)=n!r!(n−r)!
No of vacancy =12
No of candidate =25
Total no of seats of SC=5
Reserved for SC=3
No of ways of filling 3 reserved vacancies by 5 scheduled caste candidates =5C35C3
No of ways of filling rest 9 vacancies by 22 candidates =22C922C9
∴∴ Required no of ways of filling vacancies =5C3×22C95C3×22C9
Hence the given statement is false.