Question

How many four digit nos can be formed using the no 1 ,2,3,4,5 and also divisible by four

Answer 1

Answer:

24 (without repetition)

With or without repetition?  That is, are allowed to use the same digit more than once?

Here I have assumed without repetition.  Check if that's what was intended before you use this!

Step-by-step explanation:

To be divisible by 4, it must be even, so last digit must be 2 or 4.

To be divisible by 4, the last two digits must make a number divisible by 4.

If last digit is 4, third digit must be 2  (because 24 is divisible by 4, but 14, 34, 54 are not).

If last digit is 2, third digit must be 1, 3 or 5  (because 12, 32, 52 are divisible by 4, but 42 is not).

# four digit numbers

= ( # four digit numbers ending in 2) + ( # four digit numbers ending in 4 )

= ( # choices for third digit when last is 2) × ( # choices for 2nd digit ) × ( # choices for 1st digit)     + ( # choices for third digit when last is 4) × ( # choices for 2nd digit ) × ( # choices for 1st digit)

= 3 × 3 × 2  +  1 × 3 × 2

= 24