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A committee of 12 is to be formed from n...

A committee of 12 is to be formed from nine women and eight men. In how many ways this can be done if at least five women have to be included in a committee ? In how many of these committees : the men are in majority ?

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MODERN PUBLICATION-BINOMIAL THEOREM-EXERCISE
  1. The letters of the word COCHIN are permuted and all the permutations a...

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  2. The sum of series .^(20)C0-^(20)C1+^(20)C2-^(20)C3+....+^(20)C 10 is

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  3. In the binomial expansion of (a -b)^n, nge5, the sum of the 5th and 6t...

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  4. How many different words can be formed by jumbling the letters of the ...

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  5. The number of 7-digit integers, with sum of the digits equal to 10 and...

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  6. The remainder left out when 8^(2n) - (62)^(2n +1) is divided by 9 , i...

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  7. From 6 different novels and 5 different dictionaries, 4 novels and 1 d...

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  8. There are two urns. Urn A has 4 distinct red balls and urn B has 5 dis...

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  9. There are 10 points in a plane, out of these 6 are collinear. If N is ...

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  10. For r = 0 ,1,2,…, 10 , letA(r), B(r) "and " C(r) denote respectively ,...

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  11. The coefficient of x^(7) in the expansion of (1 - x- x^(2) + x^(3...

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  12. Find the number of ways in which five identical balls can be distribut...

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  13. A committee of 12 is to be formed from nine women and eight men. In ho...

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  14. A committee of 12 is to be formed from nine women and eight men. In ho...

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  15. A question paper consists of two sections having respectively 3 and 4 ...

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  16. Let R =(5 sqrt5+11)^(2n+1) and and f=R-[R], where [ ] denotes the grea...

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  17. Give that : C1+2C2 x+3C3 x^2+.....+2n. C(2n). x^(2n-1)=2n(1+x)^(2n-1)...

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  18. Prove that underset(r=1)overset(k)sum(-3)^(r-1) .^(3n)C(2r-1) = 0 , wh...

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  19. If a(0),a(1),a(2) ,…, a(2n) are the coefficients in the expansion ...

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  20. Find the value of x for which the sixth term of : (sqrt(2^(log(10-3^x)...

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