There are 9 members on a board of directors. They must form a subcommittee of 5 members. How many different subcommittees are possible?
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The combination of 'n' numbers of object taken 'r' at a time is represented by the mathematical symbol:
This can be calculated for any value of n and r as:
nCr = (nPr)/(rPr)
Where nPr is the number of permutations of n things taken r at a time. This can be calculated for any value of n and r as:
nPr = (n)*(n - 1)*(n - 2)* ... *(n - r +1)
Substituting given values of n and r in the formula for combination we get:
Number of possible different subcommittees = nCr = 9C5
= 15120/120 = 126
126 different subcommittees are possible.
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