An electric device delivers a current of [tex]$15.0 A$[/tex] for 30 seconds. How many electrons flow through it?

We need to arrange 5 letters where the first 2 are fixed, so we choose 3 from the remaining 6.
The number of ways to choose 3 letters from 6 where order matters is a permutation.
Calculate the permutation using the formula: P ( 6 , 3 ) = ( 6 − 3 )! 6 ! ​ .
The result is: 120 ​ .

Explanation

Understand the problem We are asked to find the number of ways to arrange eight letters into groups of five, where the order matters, and the first two letters are already chosen. This is a permutation problem.

Determine the remaining choices Since the first two letters are already chosen, we need to choose the remaining three letters from the remaining six letters. The order of these three letters matters.

Apply the permutation formula We need to find the number of permutations of choosing 3 letters from 6 letters. The formula for permutations is given by: P ( n , k ) = ( n − k )! n ! ​ where n is the total number of items to choose from, and k is the number of items to choose. In this case, n = 6 and k = 3 .

Calculate the permutation Plugging in the values, we get: P ( 6 , 3 ) = ( 6 − 3 )! 6 ! ​ = 3 ! 6 ! ​ = 3 × 2 × 1 6 × 5 × 4 × 3 × 2 × 1 ​ = 6 × 5 × 4 = 120 So, there are 120 ways to arrange the remaining 3 letters.

State the final answer Therefore, the number of ways to arrange eight letters into groups of five where order matters and the first two letters are already chosen is 120.


Examples
Suppose you are organizing a debate team of 5 students from a class of 8. The roles of the first two speakers have already been assigned. This problem helps you calculate how many different ways you can choose the remaining 3 speakers and assign them speaking positions.

Answered by GinnyAnswer | 2025-07-07