<u>Answer:</u> 1344 committees can be formed of four people not from one class
<u>Step-by-step explanation:</u>
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 in a committee, at least one of them are from each class
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:
- If two members come from same class
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:
- If three members come from same class
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