Question

In how many ways can a team of 3 members be formed from 3 teachers, 2 doctors and 3 accountants if at least 1 teacher must be included?

Answer 1

Answer:

46

Step-by-step explanation:

,

Answer 2

The required number of ways is 46.

Given:

Number of teachers=3

Number of doctors=2

Number of accountants=3

To find:

The number of ways of forming a team of 3 with at least 1 teacher

Solution:

We can obtain the number by using the concept of combination.

We know that nCr=n!/r!(n-r)! , where n is the total number and r is the selected or required number.

The number of teachers=3

The number of accountants and doctors=2+3=5

In a team of 3, if at least one teacher is included, the number of ways= 1 teacher out of 3×2 other people out of 5

=3C1×5C2

=3×10=30

Now, if 2 teachers are included, the number of ways = 2 teachers out of 3×1 person out of 5

=3C2×5C1

=3×5=15

When all three teachers are included, the number of ways=3C3×5C0

=1×1=1

So, the total number of ways= when 1 teacher is included+when 2 teachers are included+when 3 teachers are included

=30+15+1

=46 ways

Therefore, the required number of ways is 46.