Question

How many 3-digit even numbers will be formed using the digits 0,5,6,7 only once? (1) 10 (2) 12 (3) 14 (4) 18

please give the answer with explanation or it will be reported!​

Answer 1

Answer:

Step-by-step explanation:

The 3-digits contain 3-places.And there are 4-digits(0,5,6 and 7) to be placed in 3-places.

If we place 0 in first place (hundredths place) then it will become a 2-digit number. So 0 cannot be placed in 1st place.Therefore ,either 5 or 6 or 7 can be placed in 1st place.

No.of possibilities=3

In the second place we can place 0 or any digit (5 or 6 or 7) which must not get repeated from first place.Therefore ,No. of possibilities=3

In the third place,we can place any 2 digits(Because out of 4-digits 2 digits are placed in 1st and 2nd place).Therefore ,No.of possibilities=2

Hence number of ways to form a 3-digit number using the digits 0 , 5 , 6 ,7 only once is 3X3X2=18 ways