Permutation Combination Question 20
Question 20 - 01 February - Shift 2
The total number of six digit numbers, formed using the digits $4,5,9$ only and divisible by 6 , is ________
Show Answer
Answer: 81
Solution:
Formula: Permutation, Divisibility of numbers
Taking single digit $\rightarrow 444444 \quad \frac{6 !}{6 !}=1$ Taking two digit $\rightarrow$ $(4,5) \quad 444555 \quad (4,9) \quad 444999$
$\frac{5 !}{3 ! 2 !}=10 \quad \frac{5 !}{3 ! 2 !}=10$
Taking three digit
$ \begin{aligned} & 4,5,9,4,4,4 \Rightarrow \frac{5 !}{3 !}=20 \\ & 4,5,9,5,5,5 \Rightarrow \frac{5 !}{4 !}=5 \\ & 4,5,9,9,9,9 \Rightarrow \frac{5 !}{4 !}=5 \\ & 4,5,9,4,5,9 \Rightarrow \frac{5 !}{2 ! 2 !}=30 \\ & \text { Total = } 81 \end{aligned} $
