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`        A class has n  students. We have to form a team of the student including at least two students and also excluding atleast two student. The number of ways of forming the team is :`
one year ago

Arun
24740 Points
```							As team should consist of at least 2 and at most (n – 2) students out of n students, so required number of ways = 2 students or 3 students ........or (n – 3) students or (n – 2)students.⇒ number or ways = nC2 + nC3 + nC4 + ...... nCn – 3 + nCn – 2 ...... (I)nC0 + nC1 + nC2 + nC3 + ........ + nCn – 2 + nCn – 1 + nCn = 2n⇒ nC2 + nC3 + ......... + nCn – 2 = 2n – nC0 – nC1 – nCn–1 – nCn ⇒ nC2 + nC3 + ......... + nCn – 2 = 2n – 1 – n – n – 1⇒ nC2 + nC3 + ......... + nCn – 2 = 2n – 2n – 2 ......... (II)Substituting (II) in (I),Number of ways = 2n – 2n – 2 Hence, number of ways of forming a team: (1) 2n – 2n – 2 Hope it helps!
```
one year ago
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