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How many natural numbers less than 1000 ...

How many natural numbers less than 1000 can be formed form the digits ` 0,1,2,3,4,5` when a digit may be repeated any number of times?

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To solve the problem of how many natural numbers less than 1000 can be formed from the digits 0, 1, 2, 3, 4, and 5, where digits may be repeated, we can break it down step by step. ### Step-by-step Solution: 1. **Understanding the Range**: We need to find natural numbers that are less than 1000. This means we can have 1-digit, 2-digit, or 3-digit numbers. 2. **Counting 1-digit Numbers**: ...
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RD SHARMA-PERMUTATIONS-Solved Examples And Exercises
  1. How many numbers of four digits can be formed with the digits 1,2,3,4,...

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  2. How many three digits numbers can be formed by using the digits 0,1,...

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  3. How many natural numbers less than 1000 can be formed form the digits ...

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  4. How many five digit telephone numbers can be constructed using the dig...

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  5. Find the number of ways in which 8 distinct toys can be distributed ...

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  6. Find the number of ways in which one can post 5 letters in 7letter ...

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  7. In how many ways can 5 different balls be distributed among three bo...

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  8. In how many ways can 7 letters be posted in 4 letter boxes?

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  9. In how many ways can 4 prizes be distributed among 5 students, when No...

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  10. There are 10 lamps in a hall. Each one of them can be switched on i...

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  11. Evaluate the following: \ ^5P3

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  12. Evaluate the following: 15(P3)

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  13. Evaluate the following:5(P5)

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  14. if 5(p r)=6(p (r-1)) find r.

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  15. If 10(Pr)=5040 , find the value of rdot

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  16. If ^0P5+5^9P4=^(10)Pr , find the value of rdot

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  17. Prove the following: P(n , n)=2P(n , n-2)

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  18. Prove the following: P(n , r)=P(n-1, r)+rdotP(n-1,\ r-1)

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  19. Prove the following: n(Pn)​= n(P(n−1))

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  20. Prove the following: P(n , r)=ndotP(n-1,\ r-1)

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