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  • In how many ways 4-digit numbers can be formed using the digit 2,3,4,6,8,9 without repetition? How many of these are odd numbers?  Optio

In how many ways 4-digit numbers can be formed using the digit 2,3,4,6,8,9 without repetition? How many of these are odd numbers?

 

Option: 1

120


Option: 2

360


Option: 3

280


Option: 4

180


Answers (1)

best_answer

Using the permutation formula,

\mathrm{ ^nP_r=\frac{n!}{\left ( n-r \right )!} }

Here,

\mathrm{ n=6\ and\ r=4}

Thus,

\mathrm{ ^6P_4=\frac{6!}{\left ( 6-4 \right )!}}

 \mathrm{ ^6P_4=\frac{6!}{2!}}

\mathrm{ ^6P_4=360}

Therefore, in 360 ways the 4-digits numbers can be formed using the digit 2,3,4,6,8,9.

Here, the last digit for the odd numbers will be 3 or 9.

So, odd numbers will have the possibility of   \mathrm{^5P_3.}

Thus, the total number of odd numbers is,

\mathrm{ 2\times ^5P_3=2\times \frac{5!}{\left ( 5-3 \right )!} }

\mathrm{ 2\times ^5P_3=120}

Therefore, there are 120 odd numbers.

 

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