counting question

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counting question

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

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Other answers:

forget about the given restriction how many total ways can you arrange 5 cards in a row ?
[3] [2] [5] [9] [7] every one of this is card
how i solve it by calc plz
|dw:1441093148752:dw|
scientific calc
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 = \(5*4*3*2*1 = 120\)
card are 3 ,2,5,9,7
\(120\) is the total number of arrangements with out any restrictions
what of meaning of teamvier i m new in open study
The answer is 72...but I don't know how they got the answer not 120 i too keep the answer 120
120 is not the answer 120 is the total number of ways of arranging the given 5 cards with out any restrictions
ok how i keep the answer
72
lets find number of arrangements in which the first card is [5]
if you fix the first card as [5], how many ways can you fill in remaining 4 positions ? |dw:1441093931611:dw|
then wh
24
Yes, so there are 24 ways in which the first card can be [5]
similarly how many ways there such that last card is [5] ?
24
|dw:1441094262332:dw|
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
subtract that from the total ways, 120
72
thanks man u are the best
but what of meaning of teamvier i m new in open study

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