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  • A team of 4 students needs to be selected from a class of 7 students. However, two specific students, John and Sarah, cannot be on the team together. In how many ways can

A team of 4 students needs to be selected from a class of 7 students. However, two specific students, John and Sarah, cannot be on the team together. In how many ways can the team be formed?

Option: 1

45


Option: 2

25


Option: 3

65


Option: 4

50


Answers (1)

best_answer

Number of students = 7

Number of students to be selected = 4

Number of ways to select 4 students from 7 without John and Sarah together:

Total number of ways to form the team without any restrictions \mathrm{=C(7,4)}

Number of ways John and Sarah are together \mathrm{=C(5,2)}

Number of ways team can be formed with John and Sarah together = Total number of ways - Number of ways John and Sarah are together \mathrm{=C(7,4)-C(5,2)}

\mathrm{\text{Number of ways team can be formed = }=C(7,4)-C(5,2)=35-10=25 ways}

Hence option 2 is correct.

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Riya

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