In how many ways can the letters of the word CARPET be arranged?

Explanation:

We have 6 letters in CARPET

If we pick a letter at random, then we have 6 choices for the first slot. Then after that selection, we have 5 choices for the second (we can't reuse whatever was chosen first). Next we'd have 4 choices for the third slot, and so on.

The count down: 6,5,4,3,2,1 will multiply out to 6*5*4*3*2*1 = 720

Factorial notation shortens this, so 6! = 6*5*4*3*2*1 = 720 or we can say 6! = 120.

You can also use the permutation formula with n = 6 and r = 6 to get the same answer.

720 different combinations can be made with the letters in carpet

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step-by-step explanation:

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step-by-step explanation: