A sunday school of 12 members is to be seated on seven chairs and a bench that accomodate five persons . In how many ways can the bench be occupied?
To find the number of ways the bench can be occupied, we can use the concept of permutations.
Since there are 12 members and only 5 seats on the bench, we need to select and arrange 5 members to sit on the bench.
The formula for permutations is given by:
P(n, r) = n! / (n - r)!
Where n is the total number of items and r is the number of items selected.
Using the given formula, the number of ways to select and arrange 5 members from a group of 12 is:
P(12, 5) = 12! / (12 - 5)!
= 12! / 7!
= (12 * 11 * 10 * 9 * 8) / (5 * 4 * 3 * 2 * 1)
= 792
Therefore, there are 792 ways the bench can be occupied.