How many 3-digit even numbers can be made using the digits 1, 2, 3, 4, 6, 7, if no digit is repeated?

Asked by Pragya Singh | 1 year ago |  97

##### Solution :-

Using the numbers, 1, 2, 3, 4, 6 and 7, 3-digit numbers can be formed. The units place can be filled by any of the digits 2, 4 or 6. Hence, there are 3 ways. Since, it is given that, digits cannot be repeated, units place is already occupied, the hundreds and tens place can be occupied by remaining 5 digits. Thus, number of ways of filling hundreds and tens place

$$^5P_2=\dfrac{5!}{(5-2)!}=\dfrac{5!}{3!}$$

$$\dfrac{5\times 4\times 3!}{3!}$$

= 20

Answered by Abhisek | 1 year ago

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