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The number of different numbers that can be formed by using al

Question

The number of different numbers that can be formed by using all the digits $1, 2, 3, 4, 3, 2, 1$ , so that odd digits always occupy the odd places is

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Noah Discussed

The number of different numbers that can be formed by using all the digits

1, 2, 3, 4, 3, 2, 1

, so that odd digits always occupy the odd places is

12 mins ago

Discuss this question LIVE

12 mins ago

Text solutionVerified

One of the possible arrangements is

1

2

3

4

3

2

1

Here, the odd places are filled as

1

3

3

1

These numbers can be arranged among themselves in

\frac{4 !}{2 ! \times 2 !}

ways

The even places are filled as

2

4

2

These numbers can be arranged among themselves in

\frac{3 !}{2 !}

ways

Hence, the total number of ways is

\frac{4 !}{2 ! \times 2 !} \times \frac{3 !}{2 !} = 18

Answer is Option D

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Question Text	The number of different numbers that can be formed by using all the digits $1, 2, 3, 4, 3, 2, 1$ , so that odd digits always occupy the odd places is
Answer Type	Text solution:1
Upvotes	151