Question

using the words in the word "BACKGROUND" find the number of permutations that can be formed using 4 letters at a time

Answer 1

To find the number of permutations of 4 letters from the word "BACKGROUND", we use the permutation formula 10P4 which equals 5040 permutations.

Step-by-step explanation:

The word "BACKGROUND" consists of 10 different letters. To find the number of permutations that can be formed using 4 letters at a time, we can use the formula for permutations of n things taken r at a time, which is given by nPr = n! / (n - r)! Applying the formula for the given word:

• n (total number of letters) = 10
• r (number of letters taken at a time) = 4
• 10P4 = 10! / (10 - 4)! = 10! / 6! = 10 × 9 × 8 × 7 = 5040

So, there are 5040 different permutations of 4 letters that can be formed from the word "BACKGROUND".