Homework Help

There are 9 members on a board of directors.  They must form a subcommittee of 5...

user profile pic

torpue | Student | eNoter

Posted October 26, 2010 at 10:40 AM via web

dislike 1 like

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

1 Answer | Add Yours

user profile pic

krishna-agrawala | College Teacher | Valedictorian

Posted October 26, 2010 at 11:51 AM (Answer #1)

dislike 0 like

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.

Join to answer this question

Join a community of thousands of dedicated teachers and students.

Join eNotes