Answer :
There are 420 ways to distribute one A, three B's, two C's, and one F among seven students in a CTQR 150 class. This is calculated using the formula for permutations of a multiset. Therefore, there are 420 ways to distribute the grades among the seven students.
We need to find the number of distinct permutations of the grades among the students. Since we have a total of 7 students, and the grades are distributed as 1 A, 3 B's, 2 C's, and 1 F, this can be calculated using the formula for permutations of a multiset:
Formula: n! / (n1! * n2! * ... * nk!)
Where n is the total number of items, and n1, n2, ..., nk are the frequencies of the distinct items.
In this case, n = 7 (total students) and the frequencies are:
- 1 A
- 3 B's
- 2 C's
- 1 F
Using the formula:
=7! / (1! * 3! * 2! * 1!)
Calculating factorials:
7! = 7 × 6 × 5 × 4 × 3 × 2 × 1 = 5040
1! = 1
3! = 3 × 2 × 1 = 6
2! = 2 × 1 = 2
1! = 1
So, the number of permutations is:
=5040 / (1 × 6 × 2 × 1)
= 5040 / 12
= 420
