pleasehelpmeyes wrote:
AbhiroopGhosh wrote:
She can select the glasses in 5C3 - 3C1 ways = 7 ways
Arrangement = 7 * 3! = 42 ways
IMO B
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
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 glassesFrom a set of five glasses we can select three glasses in -
5C3 waysHowever, 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 =
3C1How ?
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 glassesThree glasses need to be arranged in a straight line = 3! ways
Hence the total = (5C3 - 3C1) * 3! ways.
Hope this helps !
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