Question

In how many ways can 6 persons be selected from 4 doctors and 8 lawyers, if atleast one doctor is included in the selection?

Answer 1

Answer:

896

Step-by-step explanation:

Hi,

Given that there are 4 doctors and 8 lawyers among which a group of 6

persons be selected such that at least one doctor is included

We can divide the above scenario into the following cases

Case 1 : 1 doctor and 5 lawyers to be selected

1 doctor out of 4 can be selected in ⁴C₁ ways = 4 ways ,

5 lawyers out of 8 can be selected in ⁸C₅ ways = 56 ways.

Number of ways in which this combination could be selected are

4*56 = 224

Case 2 : 2 doctors and 4 lawyers to be selected

2 doctors out of 4 can be selected in ⁴C₂ ways = 6 ways ,

4 lawyers out of 8 can be selected in ⁸C₄ ways = 70 ways.

Number of ways in which this combination could be selected are

6*70 = 420

Case 3 : 3 doctors and 3 lawyers to be selected

3 doctors out of 4 can be selected in ⁴C₃ ways = 4 ways ,

3 lawyers out of 8 can be selected in ⁸C₃ ways = 56 ways.

Number of ways in which this combination could be selected are

4*56 = 224

Case 4 : 4 doctors and 2 lawyers to be selected

4 doctors out of 4 can be selected in only 1 ways ,

2 lawyers out of 8 can be selected in ⁸C₂ ways = 28 ways.

Number of ways in which this combination could be selected are

1*28 = 28.

Hence, total number of ways in which this selection could happen

are (224 + 420 + 224 + 28) = 896

Hope, it helps !