There are 11 members on a board and they have to form a subcommittee of 4 how many different subcommittees are possible

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Since the problem provides the information that the subcommittees need to be different, hence, you need to use combination formula, such that:

`C(n,r) = (n!)/(r!(n-r)!), n>=r`

Since the total number of members is of 11 and the subcommittees need to contain 4 members, yields:

`C(11,4) = (11!)/(4!(11-4)!) => C(11,4) =...

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Since the problem provides the information that the subcommittees need to be different, hence, you need to use combination formula, such that:

`C(n,r) = (n!)/(r!(n-r)!), n>=r`

Since the total number of members is of 11 and the subcommittees need to contain 4 members, yields:

`C(11,4) = (11!)/(4!(11-4)!) => C(11,4) = (11!)/(4!*7!)`

`C(11,4) = (7!8*9*10*11)/(4!*7!)`

Reducing duplicate terms, yields:

`C(11,4) = (8*9*10*11)/(1*2*3*4) = 330`

Hence, evaluating the number of possible subcommittees, uunder the given conditions, yields `C(11,4) = 330` subcommittees.

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