Question

Eight persons decided to go for a picnic into two groups, one group to go by car and the other group by train. In how many ways can this be done if there must be atleast 3 persons in each group?

Answer 1

Answer:

182

Step-by-step explanation:

Hi,

Given that 8 persons decided to go for a picnic into 2 groups such that

each group consists of at least 3 persons

The above scenario can be divided into following cases

Case 1: 3 persons travel by car and 5 persons by train

3 persons to be travelling by car could be chosen in ⁸C₃ ways and

then the rest 5 would travel by train

Case 2: 4 persons travel by car and 4 persons by train

4 persons to be travelling by car could be chosen in ⁸C₄ ways and

then the rest 4 would travel by train

Case 3: 5 persons travel by car and 3 persons by train

5 persons to be travelling by car could be chosen in ⁸C₅ ways and

then the rest 3 would travel by train.

Hence, the total number of ways 8 persons can travel by grouping are

⁸C₃ + ⁸C₄ + ⁸C₅ = 182.

Hope, it helps !