A grocer wants to arrange 13 fruits in a line among which 3 are mangoes, 4 are apples, 2 are oranges, 1 pineapple and remaining are guavas. In how many different ways can he do so, if fruits of one kind are identical?	Options
A) 13!/{(2!)(3!^2)(4!)}
B) 13!/{(2!)(3!^2)}
C) 13!/{(2!)(4!)}
D) 13!
E) 13!/(3!^2)
The total number of ways in which a total N items, out of which p are identical of one type, q are identical of another type and rest are different, can be arranged in a line is N!/{p!q!}   Here we have 13 fruits out of which there are 3 alike mangoes, 4 alike apples, 2 alike oranges, 3 alike guavas and 1 pineapple.   Hence the number of ways in which he can arrange these in a line are 13!/(3!4!2!3!) = 13!/{(2!)(3!^2)(4!)}   13!/{(2!)(3!^2)(4!)}ns 13!/{(2!)(3!^2)(4!)}
<result>A</result>
A grocer wants to arrange 13 fruits in a line among which 3 are mangoes, 4 are apples, 2 are oranges, 1 pineapple and remaining are guavas. In how many different ways can he do so, if fruits of one kind are identical?