M04-14

Question

In how many ways can 5 identical blue marbles and 6 identical green marbles be arranged in a row such that all the blue marbles are grouped together?

A. 120
B. 30
C. 24
D. 11
E. 7

Bunuel · Accepted Answer

Official Solution:

In how many ways can 5 identical blue marbles and 6 identical green marbles be arranged in a row such that all the blue marbles are grouped together?

A. 120
B. 30
C. 24
D. 11
E. 7

Consider all 5 blue marbles as a single unit: {bbbbb}. Along with the 6 green marbles, we have a total of 7 units: {bbbbb}, {g}, {g}, {g}, {g}, {g}, {g}. The number of arrangements for these 7 units will be 7!/6! = 7.

Answer: E

kerin · Answer

Bunuel 
If the question had been about unique Bs & Gs, then the answer should have been 7*5!*6!, correct?

Bunuel · Answer

No, in this case the answer would be 7!*5!.

Glue b's together, we'll get 7 units:
{bbbbb}{g}{g}{g}{g}{g}{g}

# of arrangements = 7!. 5 g's within their unit can be arranged in 5! ways. So, 7!*5!.

MHIKER · Answer

Let, all the blue marbles are one, so the total element is 6+1=7, Green marbles are 6.

Here the formula is  =\frac{7!}{6!}=7

The answer is E
 https://www.youtube.com/watch?v=L81vWvqGvJ8

hirakjd · Answer

Think of the 5 identical blue marbles as one unit, so it gives us 1+6 = 7 units, these can be arranged in 7! ways BUT we have 6 identical units in these 7 units. We know that in combinatorics we have to divide by the number of identical units so the answer = 7!/6!=  7

Bunuel · Answer

I have edited the question and the solution by adding more details to enhance its clarity. I hope it is now easier to understand.

Komald · Answer

I like the solution - it’s helpful.

aastha1112 · Answer

I like the solution - it’s helpful.

Priyanshu7297 · Answer

I like the solution - it’s helpful.

karmachaser · Answer

I like the solution - it’s helpful.

M04-14

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards