To solve this problem, we need to consider the different scenarios for the number of humanities courses the student can take, which is 0, 1, or 2.

1. If the student takes 0 humanities courses, he must take 7 science courses. The number of ways to do this is C(10,7).

2. If the student takes 1 humanities course, he must take 6 science courses. The number of ways to do this is C(3,1) * C(10,6).

3. If the student takes 2 humanities courses, he must take 5 science courses. The number of ways to do this is C(3,2) * C(10,5).

The total number of ways the student can choose his courses is the sum of these three scenarios.

So, the total number of ways = C(10,7) + C(3,1)*C(10,6) + C(3,2)*C(10,5).

Here, C(n, r) is a combination which gives the number of ways of selecting r items from n different items. It is calculated as n! / [(n-r)! * r!], where "!" denotes factorial.

Question

To solve this problem, we need to consider the different scenarios for the number of humanities courses the student can take, which is 0, 1, or 2.

1. If the student takes 0 humanities courses, he must take 7 science courses. The number of ways to do this is C(10,7).

2. If the student takes 1 humanities course, he must take 6 science courses. The number of ways to do this is C(3,1) * C(10,6).

3. If the student takes 2 humanities courses, he must take 5 science courses. The number of ways to do this is C(3,2) * C(10,5).

The total number of ways the student can choose his courses is the sum of these three scenarios.

So, the total number of ways = C(10,7) + C(3,1)*C(10,6) + C(3,2)*C(10,5).

Here, C(n, r) is a combination which gives the number of ways of selecting r items from n different items. It is calculated as n! / [(n-r)! * r!], where "!" denotes factorial.

Knowee AI · Accepted Answer

To solve this problem, we need to consider the different scenarios for the number of humanities courses the student can take, which is 0, 1, or 2.

1. If the student takes 0 humanities courses, he must take 7 science courses. The number of ways to do this is C(10,7).

2. If the student takes 1 humanities course, he must take 6 science courses. The number of ways to do this is C(3,1) * C(10,6).

3. If the student takes 2 humanities courses, he must take 5 science courses. The number of ways to do this is C(3,2) * C(10,5).

The total number of ways the student can choose his courses is the sum of these three scenarios.

So, the total number of ways = C(10,7) + C(3,1)*C(10,6) + C(3,2)*C(10,5).

Here, C(n, r) is a combination which gives the number of ways of selecting r items from n different items. It is calculated as n! / [(n-r)! * r!], where "!" denotes factorial.

A university student is selecting courses for his next semester. He can choose from 3 humanities courses and 10 science courses. In how many ways can he choose 7 courses if 2 or fewer must be humanities courses?

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