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A committee of 7 peoples has to be forme...

A committee of 7 peoples has to be formed from 9 men and 4 women . In how many can this be done when then committee consists of
(i) exactly 3 women ?
(ii) at least 3 woman ?
(iii) at most 3 women ?

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The correct Answer is:
(i) The number of ways =(70)(4)=280 (ii) The number of ways (4)(70)+(1)(56)=280+56=336 (iii) `therefore` The possible ways are (1)(8)+(4)(28)+(6)(56)+(4)(70)=8+112+336+280=736 ways
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FULL MARKS-COMBINATORICS AND MATHEMATICAL INDUCTION-EXERCISE 4.3
  1. If .^(n+2) C(8) : ^((n-2)) P(4) = 57: 16 , find the value of n.

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  2. Prove that .^(2n)C(n) = ( 2^(n) xx 1 xx 3 xx …(2n-1))/(n!)

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  3. Prove that if 1 le r le n " then " n xx^((n-1))C(r-1)= (n-r+1).^(n)...

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  4. (i) A kabaddi coach has 14 players ready to play. How many different t...

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  5. Find the total number of subsets of a set with . (i) 4 elements (...

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  6. A trust has 25 members . (i) How many ways 3 officers can be sel...

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  7. How many ways a committee of six persons from 10 persons can be chosen...

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  8. How many different selections of 5 books can be made from 12 differe...

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  9. There are 5 teachers and 20 students. Out of them a committee of 2 tea...

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  10. In an examination a student has a answer 5 questions, out of 9 quest...

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  11. Determine the number of 5 card combinations out of a deck of 52 car...

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  12. Find the number of ways of forming a committee of 5 members out of...

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  13. A committee of 7 peoples has to be formed from 9 men and 4 women . In ...

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  14. 7 relatives of a man comprises 4 ladies and 3 gentlemen, his wife also...

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  15. A box contains two white balls, three black balls and four balls. In...

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  16. Find the number of strings of 4 letters that can be formed with the le...

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  17. How many triangle can be formed by joining 15 points on the plane, in ...

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  18. How many triangles can be formed by 15 points , in which 7 of them ...

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  19. There are 11 points in a plane. No three of these lies in the same ...

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  20. A polygon has 90 diagonals. Find the number of its sides ?

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