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Q.

How many 2- digit numbers can be formed from the digits {1, 2, 3, 4, and 5} without repetition and with repetition?

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a

10, 15

b

20, 25

c

30, 10

d

5, 15

answer is B.

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Detailed Solution

Given, digits {1, 2, 3, 4, and 5}.
Selection of 2- digit numbers without repetition

= {5_{P}}_{2}

= \frac{5!}{(5 - 2)!}

= \frac{5!}{3!}

= 20

Now, digits formed by repetition are {11, 22, 33, 44, and 55}.
∴ number of 2-digit numbers with repetition

= 20 + 5 = 25

Correct option is 2.

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How many 2- digit numbers can be formed from the digits {1, 2, 3, 4, and 5} without repetition and with repetition?