There are 9 members on a board of directors. They must form a subcommittee of 5 members. How many different subcommittees are possible?

Statistical Methods

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The combination of 'n' numbers of object taken 'r' at a time is represented by the mathematical symbol:

n**C**r

This can be calculated for any value of n and r as:

n**C**r = (n**P**r)/(r**P**r)

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:

n**P**r = (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 = n**C**r = 9**C**5

= (9**P**5)/(5**P**5)

= (9*8*7*6*5)/(5*4*3*2*1)

= 15120/120 = 126

Answer:

126 different subcommittees are possible.

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