Answer:
A company wants to select 3 new employees.
We have 8 candidates, 6 males, and 2 females.
1) What is the number of combinations in which the new employees can be selected?
We have 3 positions.
For the first position, we have 8 options.
For the second position, we have 7 options, because we already selected one.
For the third position, we have 6 options, because we already selected two.
The number of different combinations is (8*7*6)/(3*2*1) = 56
The division by 3*2*1 is because if we no divide by this, we are counting multiple times the same combination of employees, but they are contracted in different orders.
2) How many ways you can select only one male?
In this case, we have 3 positions, two of those positions must be for the 2 women, so in the other position, we can select only one male.
We have 6 different males for that position, so we have only 6 combinations in this case.
3) In how many ways we can select at least one male?
Previously found that we have 56 combinations in total.
We only have 2 women and 3 positions, so in all of these combinations, we have at least one male. So there are 56 combinations with at least one male.
The number of combinations in which these 3 new employees can be selected is equal to 56.
Given the following data:
Since the company needs 3 employees, it simply means there are 3 vacant positions. Thus, the number of combinations in which these 3 new employees can be selected is given by:
_nC_r = \frac{n!}{r!(n-r)!}
Combination(n, k) = n!/(r!(n - r)!)
Combination(8, 3) = 8!/(3!(8 - 3)!)
Combination(8, 3) = 8!/(3!(5)!)
Combination = (8 × 7 × 6)/(3 × 2 × 1)
Combination = 336/6
Combination = 56.
Two (2) of the 3 vacant positions must be taken by 2 women, so we can only select one male. Thus, the number of ways is given by:
Number of ways = 6 × 1
Number of ways = 6.
Choosing 1 male = 6 ways
Choosing 2 males = two males from 6 males and 1 male from two females.
Comb(6, 2) × 2 = 6!/(2!(6 - 2)!) × 2
Comb(6, 2) × 2 = 6!/(2!(4)!) × 2
Comb(6, 2) × 2 = 15 × 2
Comb(6, 2) × 2 = 30 males.
Choosing 3 males = three males from 6 males;
Comb(6, 3) = 6!/(3!(6 - 3)!)
Comb(6, 3) = 6!/(3!(3)!)
Comb(6, 3) = 20 males.
Total combination = 6 + 30 + 20
Total combination = 56.
Read more on combination here: brainly.com/question/17139330
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