Question

Consider a 8 digit no. 3681m42n where m and n are digits from 0 to 9. Find the value of m²+n if given 8 digit no. is divisible by 72.

☝️ Please help ☝️​

Answer 1

Answer:

Correct option is

B

36(7!)

S={0,1,2,3,4,5,6,7,8,9}→10digits

∑

0

9

i=45⇒ divisible by 9

∴ For 8 digit number we need to remove two digits from S

After removing ∑⇒ divisible by 9

∴ We can only remove the pairs (0,9),(1,8),(2,7),(3,6),(4,5)

Since 0+9=9,45−9=36⇒ divisible by 9

1+8=9,45−9=36⇒ divisible by 9

4+5=9

3+6=9

∴ If (0,9) are removed then no. of 8 digits nos possible =8!

if (1,8) are removed the no. of 8 digit nos =8!−7! (subtracting the number of cases where '0' is at the left most place)

Similarly, when we remove (2,7), (3,6) and (4,5) we get 8!−7! in each case.

∴ Total 8 digit nos =8!+4(8!−7!)=5⋅8!−4⋅7!

=40⋅7!−4⋅7!

=36(7!)

Answer verified by Toppr