Team of four students is to be selected from a total of 12 students for a quiz competition. In how many ways it can be selected if two particular students refuse to be together and two particular students wish to be together only in the team. .

210

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260

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226

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240

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Solution

The correct option is C
226

We suppose that student A and B wish to be selected together and students C and D don't wish to be together.

Case 1: Select all four students from remaining 8 students

Number of ways = = 70

Case 2: A and B are selected and C and D are not selected.

Select reaming 2 from reaming 8.

Number of ways = = 28

Case 3: A, B and C are selected D is not selected.

Select 1 from reaming 8.

Number of ways = = 8

Case 4: A, B and D are selected C is not selected.

Select 1 from reaming 8.

Number of ways = = 8

Case 5: D is selected and A, B and C are not selected.

Select 3 from reaming 8.

Number of ways = = 56

Case 6: C is selected and A, B and D are not selected.

Select 3 from reaming 8.

Number of ways = = 56

Total number of ways =case 1 + case 2 +case 3 +case 4 + case 5 + case 6

$= 70 + 28 + 8 + 8 + 56 + 56 = 226$

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