A company bought for its 7 offices 2 computers of brand N and 4 computers of brand M. In how many ways could computers be distributed among the offices if each office can have only 1 computer.  Options:
A) 196  B) 105  C) 256  D) 292  E) 312
This problem has to do withcombinations. Here's the general idea: if you have a set of n elements, and you are going to choose r of them (r &lt; n), then the number of combinations of size r one could choose from this total set of n is:   # of combinations = nCr = (n!)/[(r!)((n-r)!)]   where n! is the factorial symbol, which means the product of every integer from n down to 1. BTW, nCr is readn choose r.   In this problem, let's consider first the three computers of brand M. How many ways can three computer be distributed to seven offices?   # of combinations = 7C4 = 35   There are 35 different ways to distribute three computers to 7 offices. (The massive amount of cancelling that occurred there is very much typical of what happens in the nCr formula.)   One we have distributed those three M computers, we have to distribute 2 N computers to the remaining four offices. How many ways can two computer be distributed to four offices?   # of combinations = 3C2 = 3   For each of the 35 configurations of distributing the M computers, we have 3 ways of distributing the N computers to the remaining offices. Thus, the total number of configurations is 35*3= 
<gadget id="calculator">35*3</gadget>
<output>105</output>
105. Answer choice=105
<result>B</result>
A company bought for its 7 offices 2 computers of brand N and 4 computers of brand M. In how many ways could computers be distributed among the offices if each office can have only 1 computer.