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  • A team of 3 students needs to be selected from a class of 10 students. However, two specific students, John and Sarah, cannot be on the team together. In how many ways ca

A team of 3 students needs to be selected from a class of 10 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

42


Option: 2

56


Option: 3

18


Option: 4

26


Answers (1)

best_answer

\mathrm{\text{Number of students = 10}}

\mathrm{\text{Number of students to be selected = 3}}

Number of ways to select 3 students from 10 without John and Sarah together:

Selecting John:

We need to select 2 more students from the remaining 8 (excluding John and Sarah). This can be done in \mathrm{C(8,2)} ways, where \mathrm{C(n, r)} represents the number of combinations of selecting \mathrm{r} items from a set of \mathrm{n} items.

Selecting Sarah:

Similarly, we need to select 2 more students from the remaining 8 (excluding John and Sarah). This can also be done in ways.

\mathrm{\text { Total number of ways }=C(8,2)+C(8,2)=28+28=56 \mathrm{ways}}

Hence option 2 is correct.

 

Posted by

avinash.dongre

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