Question

A team consisting of a minimum of four students must be picked from a group of six students A, B, C, D, E and F. A and C must be picked together. C and E must be picked together. E and F must not be picked together.


Which of the following set of students can be picked?​

Answer 1

Answer:

Fundamental Principles of Counting

Here we shall discuss two fundamental principles viz. principle of addition and principle of multiplication.

These two principles will enable us to understand Permutations and Combinations. In fact these two principles form the base of Permutations and Combinations.

Fundamental Principle of Multiplication

"If there are two jobs such that one of them can be completed in ‘m’ ways, and another one in ‘n’ ways then the two jobs in succession can be done in ‘m X n’ ways."

Example :- In her class of 10 girls and 8 boys, the teacher has to select 1 girl AND 1 boy. In how many ways can she make her selection?

Here the teacher has to choose the pair of a girl AND a boy

For selecting a boy she has 8 options/ways AND that for a girl 10 options/ways

For 1st boy ------- any one of the 10 girls ----------- 10 ways

For 2nd boy ------- any one of the 10 girls ----------- 10 ways

For 3rd boy ------- any one of the 10 girls ----------- 10 ways

-------------

------------

For 8th boy ------- any one of the 10 girls ----------- 10 ways

Total number of ways 10 + 10 + 10 + 10 + 10 + 10 + 10 + 10 = 8b0 ways OR 10 X 8 = 80 ways.

Remark :- The above principle can be extended for any finite number of jobs.

Answer 2

Two sets of students can be picked up.

Given:

A and C must be picked together.

C and E must be picked together.

E and F must not be picked together.

To find:

Which of the sets can be picked

Solution:

We have to pick up four students, so that means 2 students have to left out.

If we pick up A, we have to pick up C too. If we pick up C we have to pick up E also.

F cannot be picked up with E

So, we have a combo of A, C AND E. For fourth member we can pick either B or D.

If we pick up B and D together, we can pick up F but we don't have a fourth member because E cannot be picked according to condition and A,C and E have to be picked up together as per condition.

Hence, two groups are A,C,E,B or A,C,E,D.

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