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How many 2 - digit numbers can be formed from the digits {1, 2

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

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

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Text solutionVerified

Forming a 2-digit number is same as finding the

2

-digit number and also it includes the arrangement of numbers.

So, we can get the number of ways to form

2

-digit number from the given set by using permutation.

Here, we have

5

digits and we need to choose

2

-digits.

Then, the number of

2

-digit numbers formed from the given set without repetition is

^{5} P_{2} = \frac{5 !}{( 5 - 2 )!} = \frac{5 !}{3 !} = 20

The numbers formed by repetition are

{11, 22, 33, 44, 55}

∴

The number of

2

-digit numbers formed from the given set with repetition

=^{5} P_{2} + 5 = 20 + 5 = 25

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Question Text	How many 2 - digit numbers can be formed from the digits {1, 2, 3, 4, 5} without repetition and with repetition?
Answer Type	Text solution:1
Upvotes	150