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In how many ways can 6 people be seated in a circle of 6 chairs? Only relative p

ID: 3006250 • Letter: I

Question

In how many ways can 6 people be seated in a circle of 6 chairs? Only relative positions in the circic can be distinguished. 9.In how many ways can first, second, and third prize in a pie-baking contest be given to 15 contestants? 10.a. Stock designations on an exchange are limited to 3 letters. How many different designations are there? b. How many different designations arc there if letters cannot be repeated? 11.In how many different ways can 19 people be seated in a row? 12.In how many different ways can 11 men and 8 women be seated in a row? 13.In how many different ways can 11 men and X women be seated in a row if the men all sit together and the women all sit together? 14.In how many different ways can 11 men and 8 women be seated in a row if no 2 women are to sit together' 15.In how many different ways can 11 men and 8 women be seated around a circular table? (Only relative positions in the circle can be distinguished.) 16.In how many different ways can 11 men and 8 women be seated around a circular table if no 2 women are to sit together? (Only relative positions in the circle can be distinguished.)

Explanation / Answer

(8)

We are given that 6 people be seated in a circle of 6 chairs

6 People in a round table can be seated in (6 - 1) ! ways = 5!

=5*4*3*2*1=120.........Answer

(12)

number of men =11

number of women =8

total number of men and women =11+8=19

so, number of ways of man and woman seating in a row =19! ........Answer

(16)

firstly arrange men, no. of ways to arrange 11 men in a round table= 10!

now, each woman will sit between two men. total space = 8 i.e M W M W M...

now, no. of ways to sit 8 women on 8 places= 8!

total no. of ways = 10! * 7! .........Answer