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Grade: 11
        
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 :
6 months ago

Answers : (1)

Arun
21037 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!

6 months ago
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