(b). A club consists of 6 freshmen, 5 sophomores, and 4 juniors. How many committees of four people not from one class

1344 committees can be formed of four people not from one class

Step-by-step explanation:

We are given:

Members in freshmen = 6

Members in sophomores = 6

Members in juniors = 6

To form a committee of four people not from one class, numerous combinations can occur. They are:

When 2 from freshmen, 1 from sophomores, and 1 from junior. The possibility becomes

When 1 from freshmen, 2 from sophomores, and 1 from junior. The possibility becomes

When 1 from freshmen, 1 from sophomores, and 2 from junior. The possibility becomes

Total combinations:

When 2 from freshmen, 2 from sophomores, and 0 from junior. The possibility becomes

When 0 from freshmen, 2 from sophomores, and 2 from junior. The possibility becomes

When 2 from freshmen, 0 from sophomores, and 2 from junior. The possibility becomes

Total combinations:

When 3 from freshmen, 1 from sophomores, and 0 from junior. The possibility becomes

When 3 from freshmen, 0 from sophomores, and 1 from junior. The possibility becomes

When 0 from freshmen, 3 from sophomores, and 1 from junior. The possibility becomes

When 1 from freshmen, 3 from sophomores, and 0 from junior. The possibility becomes

When 0 from freshmen, 1 from sophomores, and 3 from junior. The possibility becomes

When 1 from freshmen, 0 from sophomores, and 3 from junior. The possibility becomes

Total combinations:

Total number of committees that can be formed = [720 + 300 + 324] = 1344

Hence, 1344 committees can be formed of four people not from one class

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step-by-step explanation: