What is the number of permutations of the first 9 letters of the alphabet taking 5 letters at a time?

The number of permutations of the first 9 letters of the alphabet taken 5 at a time can be calculated using the formula for permutations ( P(n, r) = \frac{n!}{(n-r)!} ). Here, ( n = 9 ) and ( r = 5 ). Therefore, the calculation is ( P(9, 5) = \frac{9!}{(9-5)!} = \frac{9!}{4!} = 9 \times 8 \times 7 \times 6 \times 5 = 15,120 ). Thus, there are 15,120 permutations.