Jill bought 6 glasses for her kitchen - white, red, black, grey, yello

Total no of ways of arranging the glasses =6x5x4= 120ways
Total no of ways in which red and blue glasses can be displayed together =3!x4=24
So total no of ways in which red and blue are not together =120-24=96
So answer should be C

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The total ways of arranging the glasses are
1. Arranging 4 from white, black, grey, and yellow = 4P3
2. Selecting any 2 from white, black, grey, and yellow and 1 from red or blue = 2* 4C2*3!
= 4P3 + 2*4C2*3!= 96
Answer = C

why is it that "Total no of ways of arranging the glasses =6x5x4= 120ways
Total no of ways in which red and blue glasses can be displayed together =3!x4=24
So total no of ways in which red and blue are not together =120-24=96
So answer should be C "

i totally understand the way of the calculation except for the part where the number of red and blue glasses are subtracted

how do you build the Formular " 3!x4=24"
how do you come up with 3 and 4?
thank you

There are 3! Ways in which 3 glasses can be arranged and there are 4 ways in which the 3rd glass can be selected. So 3!x4

Sent from my Moto G (4) using GMAT Club Forum mobile app

We can use the equation:

Number of ways with red and blue glasses not together = total number of arrangements - red and blue glasses together.

Since the order of the glasses is important, we use permutations. Thus, the total number of arrangements is:

6P3 = 6!/(6-3)! = 6!/3! = 6 x 5 x 4 = 120

Since there 4 ways to choose a glass (other than red and blue) along with the red and blue glasses, and once three glasses are picked, there are 3! ways to arrange them, the number of arrangements with red and blue glasses together in a display is:

4 x 3! = 4 x 6 = 24

Thus, the number of ways with red and blue glass not together in a display is:

120 - 24 = 96

Answer: C

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