There are 7 chairs in a row. In how many ways can 3 persons occupy any three of thema)240b)210c)260d)120Correct answer is option 'B'. Can you explain this answer?

Question

Answer

Now, since the options are more and the number of students are less u can solve this question with the help of permutation and so it goes like this: since there are 7 chairs and 3 students the total number of ways will be 7P3 which gives solution as 7!/7-3! that is 7!/4! which is 7×6×5=210... hope this helps

Answer

Use permutations

Answer

First person can sit on any of the 7 seatssecond person can sit on other 6 vacant seats except one occupied by the first onesimilarly, the third can do sit on 5so, total no. of ways = 7*6*5                                      = 210therefore this is your answer

Answer

Number of ways to select 3 chairs out of 7:

To solve this problem, we can use the concept of combinations. The number of ways to select 3 chairs out of 7 is given by the formula for combinations, which is denoted as nCr, where n is the total number of items and r is the number of items to be selected. The formula for combinations is:

nCr = n! / (r!(n-r)!)

where '!' denotes the factorial operation.

In this case, we have 7 chairs and we want to select 3 of them. Plugging these values into the formula, we get:

7C3 = 7! / (3!(7-3)!)
= 7! / (3!4!)

Now, let's simplify the expression:

7! = 7 x 6 x 5 x 4 x 3 x 2 x 1
3! = 3 x 2 x 1
4! = 4 x 3 x 2 x 1

Canceling out the common factors, we have:

7C3 = (7 x 6 x 5 x 4 x 3 x 2 x 1) / (3 x 2 x 1 x 4 x 3 x 2 x 1)
= (7 x 6 x 5) / (3 x 2 x 1)
= 35

Therefore, there are 35 ways to select 3 chairs out of 7.

Number of ways to arrange the 3 persons on the selected chairs:

Once we have selected the 3 chairs, we need to arrange the 3 persons on them. Since the order of arrangement matters, we can use the concept of permutations.

The number of ways to arrange 3 persons on 3 chairs is given by the formula for permutations, which is denoted as nPr, where n is the total number of items and r is the number of items to be arranged. The formula for permutations is:

nPr = n! / (n-r)!

In this case, we have 3 persons and 3 chairs. Plugging these values into the formula, we get:

3P3 = 3! / (3-3)!
= 3! / 0!

Since 0! is defined as 1, the expression simplifies to:

3P3 = 3!

Calculating the factorial of 3:

3! = 3 x 2 x 1
= 6

Therefore, there are 6 ways to arrange the 3 persons on the selected chairs.

Total number of ways:

To find the total number of ways, we need to multiply the number of ways to select the chairs (35) by the number of ways to arrange the persons (6):

Total number of ways = 35 x 6
= 210

Hence, the correct answer is option 'B' (210).

Similar JEE Doubts

In a room there are 2 green chairs, 3 yellow chairs and 4 blue chairs. In how many ways can Raj choose 3 chairs so that at least one yellow chair is included?

In a room there are 2 green chairs, 3 yellow chairs and 4 blue chairs. In how many ways can Raj choose 3 chairs so that at least one yellow chair is included?

There are 8seats in row, where 4persons are to be seated. Then the probability of making them sit so that each person has exactly one neighbour, is

Eight chairs are numbered 1 to 8. Two women and three men wish to occupy one chair each. First the women choose the chairs from amongst the chairs marked 1 to 4 ; and then the men select the chairs from amongst the remaining. The number of possible arrangements is (1982 - 2 Marks)

Eight chairs are numbered 1 to 8. Two women and three men wish to occupy one chair each. First, the women choose the chairs from amongst the chairs marked 1 to 4 and then, the men select the chairs from amongst the remaining. The number of possible arrangements 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