counting question

- anonymous

counting question

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- schrodinger

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- anonymous

If the 5 cards shown above are placed in a row so that [5] is never at either end, how many different arrangements are possible?
The answer is 72...but I don't know how they got the answer...

- anonymous

@ganeshie8

- anonymous

[3] [2] [5] [9] [7]

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## More answers

- ganeshie8

forget about the given restriction
how many total ways can you arrange 5 cards in a row ?

- anonymous

[3] [2] [5] [9] [7] every one of this is card

- anonymous

how i solve it by calc plz

- ganeshie8

|dw:1441093148752:dw|

- anonymous

scientific calc

- ganeshie8

initially you have 5 cards available, so
you can choose the first card in 5 ways
after that, you can choose the second card in 4 ways
after that, you can choose the third card in 3 ways
after that, you can choose the fourth card in 2 ways
after that, you can choose the fifth card in 1 ways
|dw:1441093246604:dw|
so total number of ways of arranging 5 cards in a row = \(5*4*3*2*1 = 120\)

- anonymous

card are 3 ,2,5,9,7

- ganeshie8

\(120\) is the total number of arrangements with out any restrictions

- anonymous

what of meaning of teamvier i m new in open study

- anonymous

@ganeshie8

- anonymous

The answer is 72...but I don't know how they got the answer not 120 i too keep the answer 120

- anonymous

@ganeshie8

- ganeshie8

120 is not the answer
120 is the total number of ways of arranging the given 5 cards with out any restrictions

- anonymous

ok how i keep the answer

- anonymous

72

- anonymous

@@ganeshie8

- anonymous

@ganeshie8

- ganeshie8

lets find number of arrangements in which the first card is [5]

- ganeshie8

if you fix the first card as [5], how many ways can you fill in remaining 4 positions ?
|dw:1441093931611:dw|

- anonymous

then wh

- anonymous

24

- anonymous

@ganeshie8

- ganeshie8

Yes, so there are 24 ways in which the first card can be [5]

- ganeshie8

similarly how many ways there such that last card is [5] ?

- anonymous

24

- ganeshie8

|dw:1441094262332:dw|

- ganeshie8

so 24 ways in which first card is [5]
and 24 ways in which last card is [5]
thats 48 ways which we don't want

- ganeshie8

subtract that from the total ways, 120

- anonymous

72

- anonymous

thanks man u are the best

- anonymous

but what of meaning of teamvier i m new in open study

- anonymous

@ganeshie8

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