Question

How many distinct 5 digit numbers can be formed using the digits 3,2,3,2,4,5

Answer 1

Step-by-step explanation:

3,2,3,2,4,5

3_ _ _ _ _ = 5!/2! = 5×4×3 = 60

2_ _ _ _ _ = 5!/2! = 5×4×3 = 60

4_ _ _ _ _ = 5!/2!×2! = 5×2×3 = 30

5_ _ _ _ _ = 5!/2!×2! = 5×2×3 = 30

60+60+30+30 = 120+60=180 ways..

Answer 2

5 digit numbers can be formed using the digits 3,2,3,2,4,5 is 180.

Step-by-step explanation:

Given : Digits 3,2,3,2,4,5

To find : How many distinct 5 digit numbers can be formed using the digits?

Solution :

The total number are 5.

Number of ways the number form using the digit 3 is $\frac{5!}{2!}$

Number of ways the number form using the digit 2 is $\frac{5!}{2!}$

Number of ways the number form using the digit 4 is $\frac{5!}{2!\times 2!}$

Number of ways the number form using the digit 5 is $\frac{5!}{2!\times 2!}$

Total number of ways are

$n=\frac{5!}{2!}+\frac{5!}{2!}+\frac{5!}{2!\times 2!}+\frac{5!}{2!\times 2!}$

$n=\frac{5\times4\times 3\times 2\times 1}{2\times 1}+\frac{5\times4\times 3\times 2\times 1}{2\times 1}+\frac{5\times4\times 3\times 2\times 1}{2\times 1\times 2\times 1}+\frac{5\times4\times 3\times 2\times 1}{2\times 1\times 2\times 1}$

$n=5\times4\times 3+5\times4\times 3+5\times2\times 3+5\times2\times 3$

$n=60+60+30+30$

$n=180$

Therefore, 5 digit numbers can be formed using the digits 3,2,3,2,4,5 is 180.

#Learn more

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