There are 6 boys entered in the 100-meter dash. How many different ways could the come in 1st, 2nd, and 3rd? They are John, Jacob, Harry, Milton, Peter and Mike. How do I solved this problem.
order counts
6P3
To solve this problem, you need to understand the concept of permutations. In this case, we are interested in finding the number of ways in which the boys can finish 1st, 2nd, and 3rd in the 100-meter dash.
To calculate the number of permutations, you can use the formula:
nPr = n! / (n - r)!
Where "n" represents the total number of boys (6 in this case) and "r" represents the number of positions (3 in this case) to be filled.
Using this formula, you can calculate the number of permutations for this problem:
6P3 = 6! / (6 - 3)!
= 6! / 3!
= (6 * 5 * 4 * 3!) / 3!
= (6 * 5 * 4)
= 120
Therefore, there are 120 different ways the boys can come in 1st, 2nd, and 3rd in the 100-meter dash.