A group of seven mountain climbers wishes to form a mountain climbing team of five.how many different teams could be formed?
21
21
7 choose 5
= 7C5
= 7!/((7-5)!5!)
= ?
! means factorial.
35 teams
35 teams
21
The correct answer is 21.
To choose a team of 5 from a group of 7 climbers, you can use the combination formula:
nCr = n! / r!(n-r)!
where n is the total number of climbers (7) and r is the number of climbers you want to choose for the team (5).
So, 7C5 = 7! / 5!(7-5)!
= 7! / 5!2!
= (7 x 6 x 5 x 4 x 3) / (2 x 1)
= 21
Therefore, there are 21 different teams that can be formed.
To determine the number of different teams that can be formed from a group of seven mountain climbers, we can use the concept of combinations.
In this case, we need to choose 5 climbers from a group of 7. The order in which the climbers are chosen does not matter.
The formula to calculate combinations is given by:
C(n, r) = n! / (r! * (n - r)!)
Where:
- C(n, r) represents the number of combinations of choosing r items from a total of n items.
- n! denotes the factorial of n, which is the product of all positive integers up to n.
Applying this formula to our scenario, we have:
C(7, 5) = 7! / (5! * (7 - 5)!)
Calculating the factorial values:
7! = 7 * 6 * 5 * 4 * 3 * 2 * 1
5! = 5 * 4 * 3 * 2 * 1
(7 - 5)! = 2!
Now, substituting these values into the formula:
C(7, 5) = 7! / (5! * 2!)
Calculating the factorials:
7! = 5040
5! = 120
2! = 2
Substituting these values:
C(7, 5) = 5040 / (120 * 2)
C(7, 5) = 5040 / 240
C(7, 5) = 21
Therefore, there are 21 different teams that could be formed from the group of seven mountain climbers.