Selecting fruits from an urn 
An urn contains $3$ mangoes, $4$ mangoes and, $5$ oranges. Find the number of ways of selecting the fruits taking one of them at a time.

I can't quite understand the inherent meaning of this question and what I interpret is that how many different sequences of the three fruits can be built? So, the answer should be:
$$  \frac{12!}{3! \cdot 4! \cdot 5!} $$
But the book's answer is:

$$(3+1)(4+1)(5+1) - 1 = 119.$$

How are they interpreting the problem to make this the correct answer?

in the above problem they have asked the number of ways selecting the fruits taking one at a time. but you have found out the number of ways the 12 fruits can be arranged.
the interpretation of books answer is:
3 mangoes can be selected in 4 ways since we can select the 1st , 2nd or the 3rd mango or none of them....
similarly we have 5 ways for selecting next 4 mangoes and 6 ways in selecting 5 oranges. so the total no of ways is = 4*5*6 =120.
but we have included the case where we have selected none....
so the final answer is 120-1=119 ways!!
