This is a problem of permutations. We have 6 friends and we want to know in how many ways we can arrange 3 of them in 3 seats.

Step 1: Identify the number of total items (n) and the number of items to choose (r). In this case, n=6 (friends) and r=3 (seats).

Step 2: Use the formula for permutations of n items taken r at a time, which is nPr = n! / (n-r)!.

Step 3: Calculate the factorial of n (n!). In this case, 6! = 6*5*4*3*2*1 = 720.

Step 4: Calculate the factorial of (n-r) ((n-r)!). In this case, (6-3)! = 3! = 3*2*1 = 6.

Step 5: Divide the factorial of n by the factorial of (n-r) to get the number of permutations. In this case, 720 / 6 = 120.

So, the 6 friends can fill the 3 seats in the front row in 120 different ways.

Question

This is a problem of permutations. We have 6 friends and we want to know in how many ways we can arrange 3 of them in 3 seats.

Step 1: Identify the number of total items (n) and the number of items to choose (r). In this case, n=6 (friends) and r=3 (seats).

Step 2: Use the formula for permutations of n items taken r at a time, which is nPr = n! / (n-r)!.

Step 3: Calculate the factorial of n (n!). In this case, 6! = 6*5*4*3*2*1 = 720.

Step 4: Calculate the factorial of (n-r) ((n-r)!). In this case, (6-3)! = 3! = 3*2*1 = 6.

Step 5: Divide the factorial of n by the factorial of (n-r) to get the number of permutations. In this case, 720 / 6 = 120.

So, the 6 friends can fill the 3 seats in the front row in 120 different ways.

Knowee AI · Accepted Answer

This is a problem of permutations. We have 6 friends and we want to know in how many ways we can arrange 3 of them in 3 seats.

Step 1: Identify the number of total items (n) and the number of items to choose (r). In this case, n=6 (friends) and r=3 (seats).

Step 2: Use the formula for permutations of n items taken r at a time, which is nPr = n! / (n-r)!.

Step 3: Calculate the factorial of n (n!). In this case, 6! = 6*5*4*3*2*1 = 720.

Step 4: Calculate the factorial of (n-r) ((n-r)!). In this case, (6-3)! = 3! = 3*2*1 = 6.

Step 5: Divide the factorial of n by the factorial of (n-r) to get the number of permutations. In this case, 720 / 6 = 120.

So, the 6 friends can fill the 3 seats in the front row in 120 different ways.

A group of 6 friends goes to the movies, but when they get into the theater there are only 3 seats left in the front row. In how many ways can the friends fill the seats in the front row?