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Prove that there are exactly 4! numbers ...

Prove that there are exactly 4! numbers between 1000 and 10000 that contain the digits 1, 3, 5 and 7.

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MODERN PUBLICATION-PERMUTATIONS AND COMBINATIONS-EXERCISE
  1. If (n!)/(2!(n-2)!):(n!)/(4!(n-4)!) =2:1. Find the value of n.

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  2. Prove that (n!)/(r!(n-r)!)+(n!)/((r-1)!(n-r+1)!)= ((n+1)!)/ (r!(n-r+1)...

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  3. Prove that there are exactly 4! numbers between 1000 and 10000 that co...

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  4. show that 2^16 divides 32!. also, find the largest value of n for whic...

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  5. There are five colleges in a city. In how many ways can a man send 3 o...

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  6. John wants to go abroad by ship and return by air. He has a choice of ...

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  7. There are 5 routes from place A to place B and 3 routes from place B t...

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  8. If there are 20 steamers plying between places A and B, in how many wa...

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  9. If there are 20 steamers plying between places A and B, in how many wa...

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  10. In how many ways can 5 persons draw water from 5 taps, assuming no tap...

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  11. In how many ways can 3 people be seated in a row containing 7 seats ?

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  12. A sample of 3 bulbs is tested. A bulb is labelled ‘G’ if it is good a...

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  13. How many 4-letter code words are possible using the first 10 letters o...

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  14. Six pictures are to be arranged from left to right on a wall of an art...

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  15. The digits, from 0 to 9, are written on slips of paper and placed in a...

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  16. For a group photograph, 3 boys and 2 girls stand in a line in all poss...

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  17. How many 5-digit telephone numbers can be constructed using the digits...

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  18. Given (i) 4 flags (ii) 5 flags of different colours, how many differen...

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  19. Find the number of different signals that can be made by arranging at ...

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  20. How many numbers can be formed from the digits 1, 2, 3, 9 if repetitio...

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