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In how many ways may one A, three B's, two C's, and one F be distributed among seven students in a CTQR 150 class?

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

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