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Question
How many committee of five persons with a chairperson can be selected from 12 persons.
Solution
Total number of Persons = 12
Number of persons to be selected = 5
Out of 5, there is a chairperson
∴ Number of ways of selecting a chairperson = 12C1 = 12
Number of ways of selecting other 4 numbers out of remaining 11 persons = 11C4
∴ Total number of ways = 12C1 × 11C4
= `12 xx (11*10*9*8)/(4*3*2*1)`
= 12 × 330
= 3960
Hence, the required number of ways = 3960.
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