Question: How many ways can 4 people sit in a row of 6 chairs? The number of ways 4 people can sit in a row…

How many ways can 4 people sit in a row of 6 chairs? The number of ways 4 people can sit in a row of 6 chairs is \boxed{}.

Solution

To find how many ways 4 people can sit in a row of 6 chairs, we can use the concept of permutations. First, choose 4 chairs to place the people in. The number of ways to choose 4 chairs out of 6 is given by the combination: \[ \binom{6}{4} = \frac{6!}{4!(6-4)!} = \frac{6 \times 5}{2 \times 1} = 15 \] Next, arrange the 4 people in the 4 chosen chairs. The number of permutations of 4 people is given by: \[ 4! = 4 \times 3 \times 2 \times 1 = 24 \] Multiply these two results to find the total number of ways: \[ 15 \times 24 = 360 \] Therefore, the number of ways 4 people can sit in a row of 6 chairs is 360.