Question

Using the letters in the word BACKGROUND, find the number of premutations that can be formed using 4 letters at a time. Show your work or explain how you got your answer.

Answer 1

3024

Explanation:

P(n,r)= n! / (n-r)!

where n! is the factorial of n, which means the product of all positive integers less than or equal to n.

we want to find the number of permutations of 4 letters taken from the word BACKGROUND, which has 9 letters. Therefore, we can use the formula:

P(9,4)=9! (9-4)!

To simplify this expression, we can cancel out the common factors in the numerator and denominator:

P(9,4)=9×8×7×6×5!​ / 5!

P(9,4)= 9×8×7×6

P(9,4)= 3,024