Write the number of permutations in factorial form. Then simplify.
J K L M N O P
A. 7!; 720
B. 8!; 40,320
C. 7!; 49
D. 7!; 5,040
B. 8!; 40,320
To find the number of permutations in factorial form for the given letters J, K, L, M, N, O, P, we count the number of letters and calculate the factorial.
There are 7 letters in total, so the answer can be written as 7!.
Now let's simplify 7!.
7! = 7 x 6 x 5 x 4 x 3 x 2 x 1
= 5040
Therefore, the correct answer is D. 7!; 5,040.
To find the number of permutations, we need to use the factorial function. The factorial of a number is the product of all positive integers less than or equal to that number.
In this case, we have 7 letters: J, K, L, M, N, O, and P. To find the number of permutations, we start with the total number of choices (7) and multiply it by the number of choices for the next position (6), then multiply by the number of choices for the next position (5), and so on, until we reach 1.
Therefore, the number of permutations is 7! (read as "7 factorial"). Let's simplify that:
7! = 7 x 6 x 5 x 4 x 3 x 2 x 1
Now, let's calculate the value:
7 x 6 = 42
42 x 5 = 210
210 x 4 = 840
840 x 3 = 2,520
2,520 x 2 = 5,040
5,040 x 1 = 5,040
So, the correct answer is D. 7!; 5,040