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Four married couples have gathered in a room. Two persons are selected at random amongst them, find the probability that selected persons are a gentleman and a lady but not a Couple.
- a)1/7
- b)3/7
- c)1/8
- d)3/8
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
Four married couples have gathered in a room. Two persons are selected...
Solution:
Given that there are 4 married couples in the room.
We need to find the probability that the selected persons are a gentleman and a lady but not a couple.
Let's consider the total number of ways in which we can select 2 persons from 8 persons.
Total number of ways = 8C2 = (8 x 7) / (2 x 1) = 28
Case 1: Selecting a gentleman and a lady who are not a couple.
There are 4 gentlemen and 4 ladies in the room.
We can select 1 gentleman out of 4 in 4C1 ways.
We can select 1 lady out of 4 in 4C1 ways.
Out of these 2 selected persons, they should not be a couple.
There are 3 ladies for each gentleman who is not his wife.
Therefore, each gentleman has 3 choices for a lady who is not his wife.
So, the number of ways to select a gentleman and a lady who are not a couple = 4C1 x 3C1 = 12
Therefore, the probability of selecting a gentleman and a lady who are not a couple = (12/28)
Case 2: Selecting a gentleman and a lady who are a couple.
There are 4 couples in the room.
We can select 1 couple out of 4 in 4C1 ways.
We cannot select any other person along with them.
Therefore, the number of ways to select a gentleman and a lady who are a couple = 4C1 = 4
Therefore, the probability of selecting a gentleman and a lady who are a couple = (4/28)
Total probability of selecting a gentleman and a lady = Probability of case 1 + Probability of case 2
= (12/28) + (4/28)
= (16/28)
= (4/7)
Therefore, the probability of selecting a gentleman and a lady who are not a couple = (4/7) or option B.
Given that there are 4 married couples in the room.
We need to find the probability that the selected persons are a gentleman and a lady but not a couple.
Let's consider the total number of ways in which we can select 2 persons from 8 persons.
Total number of ways = 8C2 = (8 x 7) / (2 x 1) = 28
Case 1: Selecting a gentleman and a lady who are not a couple.
There are 4 gentlemen and 4 ladies in the room.
We can select 1 gentleman out of 4 in 4C1 ways.
We can select 1 lady out of 4 in 4C1 ways.
Out of these 2 selected persons, they should not be a couple.
There are 3 ladies for each gentleman who is not his wife.
Therefore, each gentleman has 3 choices for a lady who is not his wife.
So, the number of ways to select a gentleman and a lady who are not a couple = 4C1 x 3C1 = 12
Therefore, the probability of selecting a gentleman and a lady who are not a couple = (12/28)
Case 2: Selecting a gentleman and a lady who are a couple.
There are 4 couples in the room.
We can select 1 couple out of 4 in 4C1 ways.
We cannot select any other person along with them.
Therefore, the number of ways to select a gentleman and a lady who are a couple = 4C1 = 4
Therefore, the probability of selecting a gentleman and a lady who are a couple = (4/28)
Total probability of selecting a gentleman and a lady = Probability of case 1 + Probability of case 2
= (12/28) + (4/28)
= (16/28)
= (4/7)
Therefore, the probability of selecting a gentleman and a lady who are not a couple = (4/7) or option B.
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Community Answer
Four married couples have gathered in a room. Two persons are selected...
4 men,4 women
total ways =8C2=28
m1w1,m1w1,m3w3,m3w3
possible ways
m1w2,m1w3,m1w4,
m2w1,m2w3,m2w4,
m3w1,m3w2,m3w4,
m4w1,m4w2,m4w3.
12 ways
possible to get 2 person =12/28. 3/7
total ways =8C2=28
m1w1,m1w1,m3w3,m3w3
possible ways
m1w2,m1w3,m1w4,
m2w1,m2w3,m2w4,
m3w1,m3w2,m3w4,
m4w1,m4w2,m4w3.
12 ways
possible to get 2 person =12/28. 3/7
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Four married couples have gathered in a room. Two persons are selected at random amongst them, find the probability that selected persons are a gentleman and a lady but not a Couple.a)1/7b)3/7c)1/8d)3/8Correct answer is option 'B'. Can you explain this answer?
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