Combinations Examples on Couples

In this class, We discuss Combinations Examples on Couples.

The reader should have prior knowledge of combinations formulae. Click here.

Example:

Total ten couples available.

Ten couples means Ten men and ten women available.

From the above, we need to choose four of them.

1) two men and two women.

From ten men, we choose two of them in 10c2 ways.

From ten women, we chose two of them in 10c2 ways.

Total = 10c2 * 10c2

2) choose four, Two men and two women.

Condition: Do not choose a couple.

If we choose M1, i.e. men 1, we are not supposed to choose W1 because they are a couple.

When choosing two men, we need 10c2 ways.

Once we choose men, then the two women who belong to men are not considered.

When choosing two women, we need 8c2 ways.

Total = 10c2 * 8c2

3) Choose four, ie two men and two women.

Condition: Exactly one couple should be included.

First, we need to choose a couple.

We choose a couple in 10c1 ways.

Now we choose one man in 9c1 ways.

Once we choose a man, we can choose women in 8c1 ways.

Total = 10c1 * 9c1 * 8c1

4) If m1 is included then w6 should be included.

First case: m1 and w6 included.

We can choose the remaining two in 9c1 * 9c1 ways.

Second case: m1 not included.

M1 is not included; we may include or may not include w6.

If-then condition from discrete mathematics.

The second case possibility is 9c2 * 10c2.

Total = 9c1 * 9c1 + 9c2 * 10c2