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Maths, Addmaths and Statistics: Post your doubts here!

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please solve this one.
how many different odd4 digit numbers less than 4000 can be formed from the digits 1,2,3,4,5,6,7 if no digit may be repeated. please hurry

Answer 200 ??

3 Choices for the first number .. Choose 2 out of remaining 5.... 4 choices for the last number.

First Number: 1,2,3
Last Number: 1,3,5,7
Middle 2 Numbers: 2 from the rest.

in case of 1 as first number

In case of 1> 1P1*5P2*3P1 <-- Since 1 was already used. 3 remaining to choose the last from.
In case of 2> 1P1*5P2*4P1 <-- Since all the odd numbers were available. 4 remaining to choose the last from.
In case of 3> 1P1*5P2*3P1 <-- Since 3 was already used. 3 remaining to choose the last from.

Multiply them all, then add all those possibilities

(1*5P2*3P1)+(1*5P2*3P1)+(1*5P2*4P1) = 200 possible digits can be formed.
 

asd

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Answer 200 ??

3 Choices for the first number .. Choose 2 out of remaining 5 4 choices for the last number.

in case of 1 as first number

In case of 1> 1P1*5P2*3P1 <-- Since 1 was already used. 3 remaining to choose the last from.
In case of 2> 1P1*5P2*4P1 <-- Since all the odd numbers were available. 4 remaining to choose the last from.
In case of 3> 1P1*5P2*3P1 <-- Since 3 was already used. 3 remaining to choose the last from.

Multiply them all, then add all those possibilities

(1*5P2*3P1)+(1*5P2*3P1)+(1*5P2*4P1) = 200 possible digits can be formed.
you are good.
 
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Answer 200 ??

3 Choices for the first number .. Choose 2 out of remaining 5 4 choices for the last number.

in case of 1 as first number

In case of 1> 1P1*5P2*3P1 <-- Since 1 was already used. 3 remaining to choose the last from.
In case of 2> 1P1*5P2*4P1 <-- Since all the odd numbers were available. 4 remaining to choose the last from.
In case of 3> 1P1*5P2*3P1 <-- Since 3 was already used. 3 remaining to choose the last from.

Multiply them all, then add all those possibilities

(1*5P2*3P1)+(1*5P2*3P1)+(1*5P2*4P1) = 200 possible digits can be formed.
kk! almost forgot that 5P2. instead was using 2! :oops:
 
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Answer 200 ??

3 Choices for the first number .. Choose 2 out of remaining 5.... 4 choices for the last number.

First Number: 1,2,3
Last Number: 1,3,5,7
Middle 2 Numbers: 2 from the rest.

in case of 1 as first number

In case of 1> 1P1*5P2*3P1 <-- Since 1 was already used. 3 remaining to choose the last from.
In case of 2> 1P1*5P2*4P1 <-- Since all the odd numbers were available. 4 remaining to choose the last from.
In case of 3> 1P1*5P2*3P1 <-- Since 3 was already used. 3 remaining to choose the last from.

Multiply them all, then add all those possibilities

(1*5P2*3P1)+(1*5P2*3P1)+(1*5P2*4P1) = 200 possible digits can be formed.
but for selecting the first number we'll right like this 3C1 as we can chose 1 digit from the three as first digit?
 
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