The birthday of Kishore when written in ddmm format forms a four- digit number which is divisible by 9, and when written in mmdd format, forms a four-digit number which is divisible by 18. How many possibilities exist for the birthday of Kishore?
Answers
Answer:
The birthday of Kishore when written in ddmm format forms a four- digit number which is divisible by 9, and when written in mmdd format, forms a four-digit number which is divisible by 18. How many possibilities exist for the birthday of Kishore?
Explanation:
Answer:
S={0,1,2,3,4,5,6,7,8,9}→10digits
∑09i=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!)