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Bunuel
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In how many ways can 4 identical red balls and 5 different green balls 05 Feb 2021, 03:00
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75% (hard)

Question Stats:

51% (01:55) correct 49% (02:16) wrong based on 183 sessions

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In how many ways can 4 identical red balls and 5 different green balls be arranged in a line such that no two red balls are together?

A. 5*5!
B. 6*5!
C. 15*5!
D. 5*4!*5!
E. 6*4!*5!
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C
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In how many ways can 4 identical red balls and 5 different green balls 05 Feb 2021, 06:35
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Bunuel
In how many ways can 4 identical red balls and 5 different green balls be arranged in a line such that no two red balls are together?

A. 5*5!
B. 6*5!
C. 15*5!
D. 5*4!*5!
E. 6*4!*5!
Show more

Let's imagine a situation where there is one emply space between every two green balls

_ G _ G _ G _ G _ G _



Now, we have total 6 empty spaces out of which any 4 can be taken by red balls so that no two. of them are ever together

But we need only 4 spaces as we have only 4 red balls so total ways of choosing 4 spaces out of 6 \(= 6C4 = 15\)

Now, ways of arranging red balls at chosen spaces = 1 (all red balls are identical)
Now, ways of arranging Green balls at their places = 5! (all Green balls are different)

Total Outcomes \(= 6C4*1*5! = 15*5!\)

Answer: Option C
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sthahvi
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In how many ways can 4 identical red balls and 5 different green balls 05 Feb 2021, 13:01
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Bunuel
In how many ways can 4 identical red balls and 5 different green balls be arranged in a line such that no two red balls are together?

A. 5*5!
B. 6*5!
C. 15*5!
D. 5*4!*5!
E. 6*4!*5!

Let's imagine a situation where there is one emply space between every two green balls

_ G _ G _ G _ G _ G _



Now, we have total 6 empty spaces out of which any 4 can be taken by red balls so that no two. of them are ever together

But we need only 4 spaces as we have only 4 red balls so total ways of choosing 4 spaces out of 6 \(= 6C4 = 15\)

Now, ways of arranging red balls at chosen spaces = 1 (all red balls are identical)
Now, ways of arranging Green balls at their places = 5! (all Green balls are different)

Total Outcomes \(= 6C4*1*5! = 15*5!\)

Answer: Option C

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if we do it the other way around and fix the red balls such that _R_R_R_R_ then won't it be 6C5 and multiplied by 5! ?
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In how many ways can 4 identical red balls and 5 different green balls 05 Feb 2021, 22:31
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Hi sthahvi

We can try this way but then its going to be very long because there will be many cases instead of just one that you have thought

Case 1: G R G R G R G R G (No two Gs together)
Case 2: R GG R G R G R G (Two Gs together at one places)
Case 3: R GG R G R GG R (Two Gs together at two places)
Case 4: R GGG R G R G R (Three Gs together at one places)

Now you can see that you thought only the first case and not the other three which is why your answer with your calculation will be incorrect

I hope this help! :)



sthahvi
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Bunuel
In how many ways can 4 identical red balls and 5 different green balls be arranged in a line such that no two red balls are together?

A. 5*5!
B. 6*5!
C. 15*5!
D. 5*4!*5!
E. 6*4!*5!

Let's imagine a situation where there is one emply space between every two green balls

_ G _ G _ G _ G _ G _



Now, we have total 6 empty spaces out of which any 4 can be taken by red balls so that no two. of them are ever together

But we need only 4 spaces as we have only 4 red balls so total ways of choosing 4 spaces out of 6 \(= 6C4 = 15\)

Now, ways of arranging red balls at chosen spaces = 1 (all red balls are identical)
Now, ways of arranging Green balls at their places = 5! (all Green balls are different)

Total Outcomes \(= 6C4*1*5! = 15*5!\)

Answer: Option C

if we do it the other way around and fix the red balls such that _R_R_R_R_ then won't it be 6C5 and multiplied by 5! ?
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In how many ways can 4 identical red balls and 5 different green balls 27 Mar 2025, 07:05
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