Advertisements
Advertisements
Question
Delegates from 24 countries participate in a round table discussion. Find the number of seating arrangements where two specified delegates are never together.
Solution
When 2 specified delegates are never together then, the other 22 delegates can participate in a round table discussion in (22 1)! = 21! ways.
∴ There are 22 places of which any 2 places can be filled by those 2 delegates who are never together.
∴ Two specified delegates can be arranged in 22P2 ways.
∴ Total number of arrangements if two specified delegates are never together
= `""^22"P"_2xx21!`
= `(22!)/((22-2)!)xx21!`
= `(22!)/(20!)xx21!`
= 22 × 21 × 21!
= 21 × 22 × 21!
= 21 × 22!
APPEARS IN
RELATED QUESTIONS
Delegates from 24 countries participate in a round table discussion. Find the number of seating arrangements where two specified delegates are always together.
Five men, two women, and a child sit around a table. Find the number of arrangements where the child is seated between the two women.
Five men, two women, and a child sit around a table. Find the number of arrangements where the child is seated between two men.
Eight men and six women sit around a table. How many of sitting arrangements will have no two women together?
Find the number of words that can be formed by using all the letters in the word REMAIN. If these words are written in the dictionary order, what will be the 40th word?
Find the number of ways of distributing n balls in n cells. What will be the number of ways if each cell must be occupied?
Thane is the 20th station from C.S.T. If a passenger can purchase a ticket from any station to any other station, how many different ticket must be available at the booking window?
How many numbers formed using the digits 3, 2, 0, 4, 3, 2, 3 exceed one million?
Find n if 6P2 = n 6C2
Find x if nPr = x nCr
Select the correct answer from the given alternative
There are 10 persons among whom two are brothers. The total number of ways in which these persons can be seated around a round table so that exactly one person sits between the brothers is equal to:
Answer the following:
Find the value of r if 56Pr+6 : 54Pr+3 = 30800 : 1
Answer the following:
Capital English alphabet has 11 symmetric letters that appear same when looked at in a mirror. These letters are A, H, I, M, O, T, U, V, W, X, and Y. How many symmetric three letter passwords can be formed using these letters?
If r.v. X ∼ B`(n = 6, p = 1/4)`, then P(3 < X < 5) = ______
If `""^("n" - 1)"P"_4 : ""^"n""P"_5` = 1 : 6, then n = ______.
If 56Pr + 6 : 54Pr + 3 = 30800 : 1, then the value of r is ______.
