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Prove that if 1 le r le n " then " n ...

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

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Hence proved .
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SURA PUBLICATION-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. A Kabaddi coach has 14 players ready to play. How many different...

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  5. There are 15 persons in a party and if each 2 of then shakes hands w...

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  6. How many chords can be drawn through 20 points on a circle ?

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  7. In a parking lot one hundred one year old cars, are parked. Out of t...

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  8. How many ways can a team of 3 boys, 2 girls and 1 transgender be se...

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

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

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

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

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  13. There are 5 teachers and 20 students . Out of them a committee of t...

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

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

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

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

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  18. 7 relatives of a man comprises 4 ladies and 3 gentlemen, his wife also...

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

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

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