There are 6 identical chips, each of which has 1 red side and 1 blue

Question

There are 6 identical chips, each of which has 1 red side and 1 blue side. How many more ways are there to arrange the chips with 3 red sides and 3 blue sides showing than there are to arrange the chips with 4 red sides and 2 blue sides showing?

A. 3
B. 5
C. 6
D. 15
E. 20

A. 3
B. 5
C. 6
D. 15
E. 20

GMATWhizTeam · Accepted Answer

Solution: 
Since all the chips are identical and there are two colors Red and Blue, we can convert this question to a question of alphabets and words.
 • We can consider each of the chips to one alphabets and there are only two type of alphabets: R and B.
 o Now all we need to do is find the number of ways of forming words, with 3Bs, 3Rs and 2Bs, 4Rs, keeping in mind that we need to apply the concept of repetition of letters. 
 
 • 3 blue and 3 red chips: RRRBBB
 o Number of ways of arranging them =  \frac{6!}{3!*3!} = 20  
• 4 red and 2 blue chips: RRRRBB
 o Number of ways of arranging them =  \frac{6!}{4!*2!} = 15  
• Required difference = 20 – 15 = 5 
Hence, the correct answer is  Option B.

waragal · Answer

There are 6 identical chips, each of which has 1 red side and 1 blue side. How many more ways are there to arrange the chips with 3 red sides and 3 blue sides showing than there are to arrange the chips with 4 red sides and 2 blue sides showing?

A. 3
B. 5
C. 6
D. 15
E. 20

Ans:

3 red and 3 Blue

6C3  (for Selecting 3 red out of 6 chips)  x 3C3  (For selecting 3 blue out of 3 left)  =20

for 4 Red and 2 Blue
 6C4  (for Selecting 4 red out of 6 chips)  x 2C2  (For selecting 2 blue out of 2 left)  =15

Hence number of more ways are 20-15=5

Option B

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There are 6 identical chips, each of which has 1 red side and 1 blue

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