A club with 33 members is to select five officers president, vice president, sec, treasurer and historian. In how many way can the this be done.
I am not sure if I ask this before,
thank you
Since the positions are specific, this is a permutation, not a combination.
number of ways = 33*32*31*30*29
= ...
To find the number of ways to select five officers from a club with 33 members, we can use the concept of combinations.
The number of ways to select officers can be determined using the formula for combinations, which is:
C(n, r) = n! / (r! * (n - r)!)
Where n is the total number of members and r is the number of officers to be selected.
In this case, n = 33 (the total number of club members) and r = 5 (the number of officers to be selected: president, vice president, secretary, treasurer, and historian).
Plugging these values into the formula, we get:
C(33, 5) = 33! / (5! * (33 - 5)!)
Calculating the factorials:
33! = 33 * 32 * 31 * 30 * 29 * 28 * 27 * 26 * 25 * 24 * 23 * 22 * 21 * 20 * 19 * 18 * 17 * 16 * 15 * 14 * 13 * 12 * 11 * 10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1
5! = 5 * 4 * 3 * 2 * 1
(33 - 5)! = 28!
Now, we can substitute these factorial values into the formula:
C(33, 5) = 33! / (5! * 28!)
Calculating this expression will give us the total number of ways to select the five officers.