5 people, 2 couples and one single are to be seated in such a way tht couples don't sit next to each other. Wht is the probability of tht happening.
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PROBALITY
Source: Beat The GMAT — Problem Solving |
Probability that the couples are not sitting next to each other = 1 - Probability that the couples are sitting next to each other
Probability that the couples are sitting next to each other
Lets assume one couple is B1&B2 and the second couple is C1&C2 & the single is denoted by S. The number of ways we can seat them is shown below:
S C1 C2 B1 B2
C1 C2 S B1 B2
C1 C2 B1 B2 S
3 ways as shown above. Now, C1 & C2 can be arranged in 2 ways. Similarly B1 & B2 can be arranged in 2 ways. So, totally, the number of ways that the couples can sit together is = 2*2*3* = 12 ways
The number of ways both the couples & the single can be seated is = 5!/(2!*2!) = 30 ways.
So, the probability is 12/30 ==> 2/5ways
Therefore the probability of the couples not sitting together is 1-(2/5) = 3/5ways
Probability that the couples are sitting next to each other
Lets assume one couple is B1&B2 and the second couple is C1&C2 & the single is denoted by S. The number of ways we can seat them is shown below:
S C1 C2 B1 B2
C1 C2 S B1 B2
C1 C2 B1 B2 S
3 ways as shown above. Now, C1 & C2 can be arranged in 2 ways. Similarly B1 & B2 can be arranged in 2 ways. So, totally, the number of ways that the couples can sit together is = 2*2*3* = 12 ways
The number of ways both the couples & the single can be seated is = 5!/(2!*2!) = 30 ways.
So, the probability is 12/30 ==> 2/5ways
Therefore the probability of the couples not sitting together is 1-(2/5) = 3/5ways
can you explain a little bit about the 30 ways?Vemuri wrote: 3 ways as shown above. Now, C1 & C2 can be arranged in 2 ways. Similarly B1 & B2 can be arranged in 2 ways. So, totally, the number of ways that the couples can sit together is = 2*2*3* = 12 ways
The number of ways both the couples & the single can be seated is = 5!/(2!*2!) = 30 ways.
So, the probability is 12/30 ==> 2/5ways
Therefore the probability of the couples not sitting together is 1-(2/5) = 3/5ways
thanks
