Advertisements
Advertisements
Question
Eighteen guests are to be seated, half on each side of a long table. Four particular guests desire to sit on one particular 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!) (9!)(9!)`.
Options
True
False
Advertisements
Solution
This statement is True.
Explanation:
When 4 guests sit can one side and 3 on the other side
We have to select out of 11.5 sit one side and 6 sit on the other side.
Now, remaining selecting on one half side = `""^(18 - 4 - 3)"C"_5`
And the other half side = `""^((11 - 5))"C"_6` = 6C6
So, the total arrangements = 11C5 × 9! × 6C6 × 9!
= `(11!)/(5!6!) xx 9! xx 1 xx 9!`
= `(11!)/(5!6!) (9!)(9!)`
APPEARS IN
RELATED QUESTIONS
Determine n if `""^(2n)C_3 : ""^nC_3 = 11: 1`
There are four parcels and five post-offices. In how many different ways can the parcels be sent by registered post?
There are 6 multiple choice questions in an examination. How many sequences of answers are possible, if the first three questions have 4 choices each and the next three have 2 each?
There are 5 books on Mathematics and 6 books on Physics in a book shop. In how many ways can a students buy : (i) a Mathematics book and a Physics book (ii) either a Mathematics book or a Physics book?
How many three-digit odd numbers are there?
How many four-digit numbers can be formed with the digits 3, 5, 7, 8, 9 which are greater than 7000, if repetition of digits is not allowed?
How many different numbers of six digits can be formed from the digits 3, 1, 7, 0, 9, 5 when repetition of digits is not allowed?
Evaluate the following:
35C35
If nC10 = nC12, find 23Cn.
f 24Cx = 24C2x + 3, find x.
If 28C2r : 24C2r − 4 = 225 : 11, find r.
If α = mC2, then find the value of αC2.
How many different boat parties of 8, consisting of 5 boys and 3 girls, can be made from 25 boys and 10 girls?
In how many ways can a football team of 11 players be selected from 16 players? How many of these will
include 2 particular players?
There are 10 professors and 20 students out of whom a committee of 2 professors and 3 students is to be formed. Find the number of ways in which this can be done. Further find in how many of these committees:
a particular student is included.
From 4 officers and 8 jawans in how many ways can 6 be chosen. to include at least one officer?
Find the number of diagonals of , 1.a hexagon
How many triangles can be obtained by joining 12 points, five of which are collinear?
A group consists of 4 girls and 7 boys. In how many ways can a team of 5 members be selected if the team has(iii) at least 3 girls?
Find the number of ways of selecting 9 balls from 6 red balls, 5 white balls and 5 blue balls if each selection consists of 3 balls of each colour.
In how many ways can one select a cricket team of eleven from 17 players in which only 5 persons can bowl if each cricket team of 11 must include exactly 4 bowlers?
A parallelogram is cut by two sets of m lines parallel to its sides. Find the number of parallelograms thus formed.
How many different words, each containing 2 vowels and 3 consonants can be formed with 5 vowels and 17 consonants?
Find the number of combinations and permutations of 4 letters taken from the word 'EXAMINATION'.
In how many ways can a committee of 5 be made out of 6 men and 4 women containing at least one women?
The number of ways in which a host lady can invite for a party of 8 out of 12 people of whom two do not want to attend the party together is
Among 14 players, 5 are bowlers. In how many ways a team of 11 may be formed with at least 4 bowlers?
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
If n + 1C3 = 2 · nC2 , then n =
Find the number of ways of drawing 9 balls from a bag that has 6 red balls, 5 green balls, and 7 blue balls so that 3 balls of every colour are drawn.
Find the value of 20C16 – 19C16
Answer the following:
A question paper has 6 questions. How many ways does a student have to answer if he wants to solve at least one question?
If α = mC2, then αC2 is equal to.
In how many ways can the letters of the word 'IMAGE' be arranged so that the vowels should always occupy odd places?
A student has to answer 10 questions, choosing atleast 4 from each of Parts A and B. If there are 6 questions in Part A and 7 in Part B, in how many ways can the student choose 10 questions?
If nCr – 1 = 36, nCr = 84 and nCr + 1 = 126, then find rC2.
Given 5 different green dyes, four different blue dyes and three different red dyes, the number of combinations of dyes which can be chosen taking at least one green and one blue dye is ______.
A candidate is required to answer 7 questions out of 12 questions which are divided into two groups, each containing 6 questions. He is not permitted to attempt more than 5 questions from either group. He can choose the seven questions in 650 ways.
