Tanya bought 5 glasses for her kitchen - white, red, black, grey, and

Question

Tanya bought 5 glasses for her kitchen - white, red, black, grey, and blue - and would like to display 3 of them on the shelf next to each other. If she decides that a black and a white glass cannot be displayed at the same time, in how many different ways can Tanya arrange the glasses?

A. 36
B. 42
C. 48
D. 54
E. 72

A. 36
B. 42
C. 48
D. 54
E. 72

gmatophobia · Answer

She can select the glasses in 5C3 - 3C1 ways = 7 ways

Arrangement = 7 * 3! = 42 ways

IMO B

pleasehelpmeyes · Answer

This is how I worked it out but your way is far more efficient could you explain in words how that works I would love to cut down this time wasted.

So we have 3 possible outcomes
1: No Black
2: No White
3: Neither Black nor White

1: No Black is given so we can find the number of combinations by taking white as given in the 3 different positions (1)(3)(2) + (3)(1)(2) + (3)(2)(1) = 18
2: Similarly No White will be 18 as well 
3. Neither black nor white is just 3! since we are only left with 3 variables to put into 3 possible combinations.

Add them together and there is 42 possible outcomes, therefore B

gmatophobia · Answer

pleasehelpmeyes  - Thank you for sharing your approach. The approach definitely looks good !

You divided the problem and used the principle of counting to obtain the total.

Here are few details on my working -

Given  - 
Tanya has white, red, black, grey, and blue.
She wants to arrange 3 of them on the shelf next to each other. Hence, she wants to arrange the glasses in a straight line.
 Condition  : A black and a white glass cannot be displayed at the same time.

Thus, there are two parts to this problem -
1) Selecting three glasses, out of the five that she bought (adhering to the condition)
2) Arranging the three selected glasses in a straight line.

Selecting three glasses

From a set of five glasses we can select three glasses in -  5C3 ways

However, this will also involve a selection where a black and a white glass have been selected. So we need to substract this from the selection.

Number of ways of selecting three glasses from a set of five glasses such that a black and a white glass is always selected =  3C1

How ?
After the black and the white glass is selected we have only selection to be done from the remaining 3 glasses.

So total ways of selecting the glasses = 5C3 - 3C1 ways

Arranging the three selected glasses

Three glasses need to be arranged in a straight line = 3! ways

Hence the total = (5C3 - 3C1) * 3! ways.

Hope this helps !

KarishmaB · Answer

There are 5 colours and 2 cannot be chosen together so from our selection, we need to remove those cases in which both white and black are chosen together. Total number of selections = 5C3 = 10 Number of selections that are not acceptable = Select white, black and any one of the remaining 3 colours in 3C1 = 3 ways Acceptable selections = 10 - 3 = 7 Number of ways in which we can arrange = 3! = 6 Total number of arrangements = 7*6 = 42 Answer (B) Video on Permutations: https://youtu.be/LFnLKx06EMU Video on Combinations: https://youtu.be/tUPJhcUxllQ

pleasehelpmeyes · Answer

This makes perfect sense, thanks a million!

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Tanya bought 5 glasses for her kitchen - white, red, black, grey, and

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Tanya bought 5 glasses for her kitchen - white, red, black, grey, and

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