At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
If the 5 cards shown above are placed in a row so that  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...
    
forget about the given restriction how many total ways can you arrange 5 cards in a row ?
     every one of this is card
how i solve it by calc plz
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
lets find number of arrangements in which the first card is 
if you fix the first card as , how many ways can you fill in remaining 4 positions ? |dw:1441093931611:dw|
Yes, so there are 24 ways in which the first card can be 
similarly how many ways there such that last card is  ?
so 24 ways in which first card is  and 24 ways in which last card is  thats 48 ways which we don't want
subtract that from the total ways, 120
thanks man u are the best
but what of meaning of teamvier i m new in open study