Final answer:
To find the number of different 10-letter words that can be formed from the letters provided, considering the repetition of the letter 'P', we calculate 10! / 2!, resulting in 1,814,400 different words.
Step-by-step explanation:
The question asks how many different 10-letter words can be formed from the letters R, P, C, Z, G, V, P, A, Q, Y. Since the letter 'P' is repeated twice, the formula used to calculate the permutations of the letters needs to account for this repetition. Normally, the number of permutations of 'n' distinct objects is 'n!'. However, if there are duplicate objects, the formula becomes 'n!' divided by the factorial of the number of times each duplicate object occurs. In this case, we have 10 letters with 'P' occurring twice, so the formula is 10! / 2!.
The calculation is therefore:
- 10! is 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 3,628,800
- 2! is 2 x 1 = 2
- Permutations = 10! / 2! = 3,628,800 / 2 = 1,814,400
So, we have 1,814,400 different 10-letter words that can be formed from the given letters.