20. A company must select 3 employees from a department that has a total of 5 employees
to attend a workshop in quality management. The number of possible selections are
(a) 15.
(b) 60.
(c) 10.
(d) 20.
21. From a group of 5 men and 4 women, a committee is to be formed consisting of 2 men
and 2 women. The number of possible ways this committee can be formed:
(a) 4.
(b) 30.
(c) 10.
(d) 60.
To find the number of possible selections or ways, we can use the concept of combinations.
For question 20:
Here, we need to select 3 employees from a department with 5 employees to attend the workshop.
The number of ways to choose 3 employees from 5 can be calculated using the combination formula:
C(n, r) = n! / (r! * (n-r)!)
In this case, n = 5 (total number of employees in the department) and r = 3 (number of employees to be selected).
So, the number of possible selections is C(5, 3) = 5! / (3! * (5-3)!) = (5 * 4 * 3!) / (3! * 2 * 1) = 5 * 4 / (2 * 1) = 10.
Therefore, the answer for question 20 is (c) 10.
For question 21:
Here, we need to form a committee with 2 men and 2 women from a group of 5 men and 4 women.
The number of ways to choose 2 men from 5 and 2 women from 4 can be calculated separately using the combination formula, and then, to find the total number of ways, we can multiply the results together.
Number of ways to select 2 men from 5: C(5, 2) = 5! / (2! * (5-2)!) = (5 * 4 * 3!) / (2! * 3!) = 5 * 4 / (2 * 1) = 10.
Number of ways to select 2 women from 4: C(4, 2) = 4! / (2! * (4-2)!) = (4 * 3 * 2!) / (2! * 2 * 1) = 4 * 3 / (2 * 1) = 6.
Total number of ways to form the committee = number of ways to select 2 men * number of ways to select 2 women = 10 * 6 = 60.
Therefore, the answer for question 21 is (d) 60.