how many four letter words can be made fro the letters p,a,y,m,e,n,t with no repetition of any letters?
To find the number of four-letter words that can be made from the letters P, A, Y, M, E, N, T without repetition, we can use the concept of permutations.
A permutation is an arrangement of objects without repetition, where the order matters. In this case, we want to arrange 4 letters out of the 6 given letters.
To calculate the number of permutations, we can use the formula:
nPr = n! / (n - r)!
n represents the total number of objects (in this case, letters), and r represents the number of objects to be selected (in this case, 4 letters).
For our example, n = 6 (since we have 6 letters) and r = 4 (since we want to arrange 4 letters). Plugging the values into the formula:
6P4 = 6! / (6 - 4)!
= 6! / 2!
= (6 × 5 × 4 × 3 × 2 × 1) / (2 × 1)
= (720) / (2)
= 360
Therefore, there are 360 different four-letter words that can be made from the letters P, A, Y, M, E, N, T without repetition.
Find the _permutations_ of 4 elements selected without repetition from a set of 7.
^7P_4