How many five-letter sequences are possible that use the letters a, p, j, e, x once each?
so you are just arranging all the letters
a,p,j,e,x
that would be 5! or 120
120
To find the number of five-letter sequences that can be formed using the letters a, p, j, e, and x once each, we can use the concept of permutations.
A permutation is an arrangement of objects in a specific order. For our case, we want to find the number of permutations of the five letters.
To calculate the number of permutations, we can use the formula:
nPr = n! / (n - r)!
where n is the total number of distinct objects (in this case, 5 letters) and r is the number of objects we want to arrange (in this case, 5 letters as well).
Let's substitute the values into the formula:
5P5 = 5! / (5 - 5)!
= 5! / 0!
= 5! / 1
= 5 * 4 * 3 * 2 * 1 / 1
= 5 * 4 * 3 * 2
= 120
Hence, there are 120 possible five-letter sequences that can be formed using the letters a, p, j, e, and x once each.