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  • The total number of six digit numbers, formed using the digits 4, 5, 9 only and divisible by 6 , isOption: 1 81

The total number of six digit numbers, formed using the digits 4, 5, 9 only and divisible by 6 , is

Option: 1

81


Option: 2

__


Option: 3

__


Option: 4

__


Answers (1)

best_answer

We have,
For this, 4 will be fixed as unit place digit

Case I: 4^{\prime} s \rightarrow 6 times\\ Case II: \quad 4$ 's $\rightarrow 4 times

\begin{aligned} &5^{\prime} s \rightarrow 1 \text { times } \quad \frac{5 !}{3 !}=20\\ &9^{\prime} s \rightarrow 1 \text { times } \end{aligned}

\text { Case III: } \quad 4^{\prime} s \rightarrow 3 \text { times }

5^{\prime} s \rightarrow 3 \text { times } \quad \frac{5 !}{2 ! 3 !}=10

\text { Case IV: } \quad 4 \text { 's } \rightarrow \text { 3times }

9^{\prime} s \rightarrow 3 \text { times } \quad \frac{5 !}{2 ! 3 !}=10

\text { Case } V: \quad 4^{\prime} s \rightarrow 2 \text { times }

\begin{aligned} & 5^{\prime} s \rightarrow 2 \text { times } \quad \frac{5 !}{2 ! 2 !}=30 \\ & 9^{\prime} s \rightarrow 2 \text { times } \end{aligned}

\text { Case VI: } \quad 4^{\prime} s \rightarrow 1 \text { times }

\begin{aligned} & 5 \text { 's } \rightarrow 1 \text { times } \quad \frac{5 !}{4 !}=5 \\ & 9 \text { 's } \rightarrow \text { 4times } \end{aligned}

\text { Case VII: } 4 \text { 's } \rightarrow 1 \text { times }

\begin{aligned} & 5^{\prime} s \rightarrow 4 \text { times } \quad \frac{5 !}{4 !}=5 \\ & 9^{\prime} s \rightarrow 1 \text { times } \end{aligned}

Total numbers =81

 

 

 

Posted by

Devendra Khairwa

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