A lady arranges a dinner party for 6 guests .The number of ways in which they may be selected from among 10 friends if 2 of the friends will not attend the party together isa)164b)140c)112d)none of theseCorrect answer is option 'B'. Can you explain this answer?

Question

Answer

Let us say that the two particular friends are A and B.
If A is invited among six guests and B is not, then: number of combinations to select 5 more guests from the remaining 8 friends:
C(8, 5) = 8 ! / (5! 3!) = 56
If B is invited among the six guests and A is not , then the number of ways of selecting the remaining 5 guests = C(8, 5) = 56
Suppose both A and B are not included in the six guests list : then the number of such combinations = C(8, 6) = 7 * 8 /2 = 28
So the total number of sets of guests that can be selected = 140.

Answer

Answer

To solve this problem, we can use the concept of combinations and the principle of inclusion-exclusion.

Given:
- Number of friends = 10
- Number of guests at the dinner party = 6
- 2 friends will not attend the party together

First, let's calculate the total number of ways to select 6 guests from 10 friends without any restrictions.

Total ways to select 6 guests from 10 friends = C(10, 6)
= 10! / (6! * (10-6)!)
= 10! / (6! * 4!)
= (10 * 9 * 8 * 7) / (4 * 3 * 2 * 1)
= 210

Now, let's consider the restriction that 2 friends will not attend the party together. We can use the principle of inclusion-exclusion to calculate the number of ways to select the guests while satisfying this restriction.

Let's assume the two friends who cannot attend the party together as A and B.

Step 1: Calculate the number of ways to select 6 guests without considering the restriction.
= Total ways to select 6 guests from 10 friends
= 210

Step 2: Calculate the number of ways to select 6 guests where both A and B are present.
We need to select 4 guests from the remaining 8 friends (excluding A and B).
= C(8, 4)
= 8! / (4! * (8-4)!)
= (8 * 7 * 6 * 5) / (4 * 3 * 2 * 1)
= 70

Step 3: Calculate the number of ways to select 6 guests where both A and B are absent.
We need to select 6 guests from the remaining 8 friends (excluding A and B).
= C(8, 6)
= 8! / (6! * (8-6)!)
= (8 * 7) / (2 * 1)
= 28

Step 4: Calculate the number of ways to select 6 guests where either A or B is absent.
= Total ways to select 6 guests from 10 friends - Number of ways where both A and B are present - Number of ways where both A and B are absent
= 210 - 70 - 28
= 112

Therefore, the number of ways to select 6 guests from among 10 friends, where 2 friends will not attend the party together, is 112 (option C).

Answer

Please see the detailed solution..

Answer

HoW?????

Similar JEE Doubts

A lady arranges a dinner party for 6 guests .The number of ways in which they may be selected from among 10 friends if 2 of the friends will not attend the party together is

A lady gives a dinner party to six guests. The number of ways in which they may be selected from among ten friends, if two of the friends will not attend the party together is

A lady gives a dinner party for six guests.the number of ways in which they may be selected from among ten friends,if two of the friends will not attend the party together is

A person invites a party of 10 friends at dinner and place them so that 4 are on one round table and 6 on the other round table. The number of ways in which he can arrange the guests is

Top Courses for JEEView all

Physics for JEE Main & Advanced

Mock Tests for JEE Main and Advanced 2025

Mathematics (Maths) for JEE Main & Advanced

Chemistry for JEE Main & Advanced

Study Plan for JEE

Top Courses for JEE

Top Courses for JEE

Related Content

JEE Courses

Mock Test Series

Past Year Papers

Additional Courses

Company