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Discussion Response Post to: permututions & combination... sums...

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1)No. of ways of selecting 1st couple = ¹⁵C_1.¹⁵C₁

No. of ways of selecting 2nd couple =¹⁴C₁¹⁴C₁

and so on... therefore total ways = ¹⁵C_1.¹⁵C₁+¹⁴C1_.¹⁴C₁+and so on till ¹C₁.¹C₁

= 15^2+14^2+13^2..............1^2 = n.(n+1)(2*n+1)/6 = 15.16.31/6 = 1240 (a)

2) No. of students answering atleast n questions wrong = 2ⁿ

No. of students answering atleast n-1 questions wrong = 2^n-1

No. of students answering atleast n-2 questions wrong = 2^n-2

^{.......................................}

No. of students answering atleast 1 questions wrong = 2¹

No. of students answering 1 questions wrong = 2ⁿ-2^n-1*1...................similarly for other till n question wrong.

therefore total no. of wrong ans. = On simplifying......2ⁿ+2^n-1+2^n-2+........2+1

solving as G.P we get n = 13

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