Home
Class 12
MATHS
A tea party is arranged for 16 persons a...

A tea party is arranged for 16 persons along two sides of a long table with 8 chairs on each side. Four persons wish to sit on one particular and two on the other side. In how many ways can they be seated?

Text Solution

Verified by Experts

The correct Answer is:
`.^(8)P_(4)xx.^(8)P_(2)xx10!`
There are 8 chairs on each side of the table. Let sides be represented by A and B. let four persons sit on side A, then number of ways arranging 4 persons on 8 chairs on side `A=.^(8)P_(4)` and then two persons sit on side B, then number of ways arranging 2 persons on 8 chairs on side `B=.^(8)P_(2)` and arranging the remaining 10 persons in remaining 10 chairs in 10! ways.
hence, the total number of ways in which the persons can be arranged`=.^(8)P_(4)xx.^(8)P_(2)xx10!=(8!*8!*10!)/(4!6!)`
Promotional Banner

Similar Questions

Explore conceptually related problems

Eighteen guests are to be seated, half on each side of a long table. Four particular guests desire to sit on one p[articular side and three others on other side of the table. The number of ways in which the seating arrangements can be made is (11!)/(5!6!)xx 9!xx 9!.

We wish tto select 6 person from 8 but, if the person A is chosen, then B must be chosen. In how many ways can selections be made ?

In how many ways can 15 members of a council sit along a circular table, when the secretary is to sit on one side of the chairman and the deputy secretary on the other side?

A boat is to be manned by eight men, of whom 2 can only row on bow side and 1 can only row on stroke side; in how many ways can the crew be arranged?

A family consists of a grandfather, 5 sons and daughters and 8 grand child. They are to be seated in a row for dinner. The grand children wish to occupy the 4 seats at each end and the grandfather refuses to have a grandchild on either side of him. In how many ways can the family be made to sit?

Seven persons are to be seated in a row. The probability that two particular persons sit next to each other is

If two sides of a triangle measure 4 cm and 6 cm find all possible measurements (positive Integers) of the third side. How many distinct triangles can be obtained?

Consider a disc rotating in the horizontal plane with a constant angular speed omega about its centre O . The disc has a shaded region on one side of the diameter and an unshaded region on the other side as shown in the figure. When the disc is in the orientation as shown, two pebbles P and Q are simultaneously projected at an angle towards R. The velocity of projection is in the y-z plane and is same for both pebbles with respect to the disc. Assume that (i) they land back on the disc before the disc has completed (1)/(8) rotation, (ii) their range is less than half the disc radius, and (iii) w remains constant throughout. Then

A question paper consists of two sections having respectively, 3 and 5 questions. The followinng note is given on the paper "it is not necessory to attempt all the questions one questions from each section is compulsory". In how many ways can candidate select the questions?

Once again you are given four cards. Each card has a number printed on one side and a letter on the other side. Which are the only two cards you need to turn over to check whether the following rule holds? "If a card has a consonant on one side, then it has an odd number on the other side."