Hi,

In total there are 5 members to be selected out of 12.

If all 12 members were the same then the choice would have been 12C5, i.e. Option A.

But all members are not the same since there are two maned positions namely president and vice president.

If all the positions were distict the choice 12P5 would be correct, i.e. Option D would have been right.

There are only 2 named positions and 3 non named positions.

No of ways to select a president= 12.

No of ways to select a vice president =11.

No of ways to select 3 members from the remaining 10 is 10C3= \(\frac{10!}{7! \times 3!}\)

Hence number of ways to selct president, vice president and 3 members = \(12 \times 11 \times\frac{10!}{7! \times 3!}\)= \(\frac{12!}{7! \times 3!}\).

Hence option B is correct!
_________________

Sandy

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