If a team of 5 is to be formed from 12 candidates, how many different teams can be formed?

Using the combination formula: 
C(12, 5) 
= 12! / (5!(12-5)!) 
= 12! / (5!7!) 
= 792. 
Therefore, 792 different teams can be formed.

If 10 students need to form a project team of 3, how many different teams can they form?

Using the combination formula: 
C(10, 3) 
= 10! / (3!(10-3)!) 
= 120. 
Therefore, they can form 120 different teams.

How can you form a team of 4 from 8 people, ensuring that 2 specific people are always included?

If 2 people are always included, you need to select 2 more from the remaining 6. 
The number of ways is C(6, 2) = 15.

In a quiz competition, 5 members are to be selected from a group of 15 participants. How many teams can be formed?

Using the combination formula: 
C(15, 5) 
= 15! / (5!(15-5)!) 
= 3003. 
Thus, 3003 different teams can be formed.

If you need to form a mixed team of 2 men and 2 women from a pool of 6 men and 5 women, how many different combinations can you create?

Calculate the combinations separately: C(6, 2) for men 
and 
C(5, 2) for women. 
The total combinations 
= C(6, 2) * C(5, 2) 
= 15 * 10 
= 150.

What is the total number of ways to form a team of 4 from 9 people if one specific person must be included?

If one person is included, you must choose 3 from the remaining 8. 
The total ways 
= C(8, 3) 
= 56.

If there are 10 candidates and you want to form a team of 2, but one candidate must always be included, how many teams can be formed?

Fix that candidate and select 1 from the remaining 9: 
C(9, 1) = 9. 
Thus, there are 9 teams.

If a committee of 5 is formed from 8 men and 7 women, ensuring that there are at least 3 women, how do you calculate the number of combinations?

Calculate the combinations for 3, 4, and 5 women separately and sum them up: 
C(7, 3) * C(8, 2) + C(7, 4) * C(8, 1) + C(7, 5).