9 people are to be divided into a group of 4, a group of 3 and a group of 2. In how many different ways can this be done?
Solution
To divide 9 people into groups of 4, 3, and 2, we use combinations.
First, choose 4 people out of 9 for the first group: \(\binom{9}{4}\).
Then, choose 3 people out of the remaining 5 for the second group: \(\binom{5}{3}\).
The last 2 people automatically form the third group: \(\binom{2}{2}\).
Calculate each combination:
\(\binom{9}{4} = 126\)
\(\binom{5}{3} = 10\)
\(\binom{2}{2} = 1\)
Multiply these results to find the total number of ways:
\(126 \times 10 \times 1 = 1260\)
Log in to record attempts.