Is there a quick way to do this?
In how many different ways can 1st, 2nd, and 3rd place ribbons be given to 7 finalists in a game?
assistance needed
ist place can be given to 7 different people, and then 2nd place can be given to 6 different people, followed by 3rd, which can now be given to one of the remaining 5 people, so
number of different ways = 7*6*5 = 210
Find the greatest common factor of 43 and 32
Yes, there is a quick way to find the number of different ways 1st, 2nd, and 3rd place ribbons can be given to 7 finalists in a game. This can be determined using the concept of permutations.
To find the number of ways, we can use the formula for permutations of n objects taken r at a time, which is given by:
P(n, r) = n! / (n - r)!
In this case, we have 7 finalists eligible for the 1st place ribbon, 6 remaining finalists eligible for the 2nd place ribbon, and 5 remaining finalists eligible for the 3rd place ribbon.
So, the number of ways to give the ribbons can be calculated as:
P(7, 3) = 7! / (7 - 3)! = 7! / 4!
Simplifying this expression, we get:
P(7, 3) = (7 * 6 * 5 * 4 * 3 * 2 * 1) / (4 * 3 * 2 * 1)
Now, we can cancel out the terms:
P(7, 3) = (7 * 6 * 5) / (3 * 2 * 1)
Evaluating this expression, we find:
P(7, 3) = 210
Therefore, there are 210 different ways to give the 1st, 2nd, and 3rd place ribbons to 7 finalists in the game.