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How many numbers of four digits can be f...

How many numbers of four digits can be formed with the digits `1,2,3,4,5` if the digits can be repeated in the same number?

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To solve the problem of how many four-digit numbers can be formed using the digits `1, 2, 3, 4, 5` with repetition allowed, we can follow these steps: ### Step-by-Step Solution: 1. **Identify the Digits Available**: The digits we can use are `1, 2, 3, 4, 5`. This gives us a total of 5 different digits. 2. **Determine the Number of Positions**: We need to form a four-digit number. This means we have 4 positions to fill (thousands, hundreds, tens, and units). ...
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RD SHARMA-PERMUTATIONS-Solved Examples And Exercises
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  12. There are 10 lamps in a hall. Each one of them can be switched on i...

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  13. Evaluate the following: \ ^5P3

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  14. Evaluate the following: 15(P3)

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  15. Evaluate the following:5(P5)

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

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

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

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

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

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