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

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

nCr

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

=
(9P5)/(5P5)

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

= 15120/120 =
126

Answer:

126 different
subcommittees are possible.