Advertisements
Advertisements
प्रश्न
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!)`.
पर्याय
True
False
Advertisements
उत्तर
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
संबंधित प्रश्न
Determine the number of 5 card combinations out of a deck of 52 cards if there is exactly one ace in each combination.
The English alphabet has 5 vowels and 21 consonants. How many words with two different vowels and 2 different consonants can be formed from the alphabet?
Determine the number of 5-card combinations out of a deck of 52 cards if each selection of 5 cards has exactly one king.
Compute:
L.C.M. (6!, 7!, 8!)
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 numbers are there?
Evaluate the following:
n + 1Cn
If nC10 = nC12, find 23Cn.
f 24Cx = 24C2x + 3, find x.
If 15C3r = 15Cr + 3, find r.
If nC4 , nC5 and nC6 are in A.P., then find n.
From a group of 15 cricket players, a team of 11 players is to be chosen. In how many ways can this be done?
In how many ways can a football team of 11 players be selected from 16 players? How many of these will
exclude 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 excluded.
From a class of 12 boys and 10 girls, 10 students are to be chosen for a competition; at least including 4 boys and 4 girls. The 2 girls who won the prizes last year should be included. In how many ways can the selection be made?
How many different selections of 4 books can be made from 10 different books, if
two particular books are always selected;
Find the number of ways in which : (a) a selection
If 20Cr + 1 = 20Cr − 1 , then r is equal to
If nC12 = nC8 , then n =
In how many ways can a committee of 5 be made out of 6 men and 4 women containing at least one women?
There are 10 points in a plane and 4 of them are collinear. The number of straight lines joining any two of them is
Given 11 points, of which 5 lie on one circle, other than these 5, no 4 lie on one circle. Then the number of circles that can be drawn so that each contains at least 3 of the given points is
The number of diagonals that can be drawn by joining the vertices of an octagon is
The number of parallelograms that can be formed from a set of four parallel lines intersecting another set of three parallel lines is
Find the number of ways of dividing 20 objects in three groups of sizes 8, 7, and 5.
Find the value of 80C2
The value of `(""^9"C"_0 + ""^9"C"_1) + (""^9"C"_1 + ""^9"C"_2) + ... + (""^9"C"_8 + ""^9"C"_9)` is ______
In how many ways a committee consisting of 3 men and 2 women, can be chosen from 7 men and 5 women?
We wish to select 6 persons from 8, but if the person A is chosen, then B must be chosen. In how many ways can selections be made?
There are 10 lamps in a hall. Each one of them can be switched on independently. Find the number of ways in which the hall can be illuminated.
A convex polygon has 44 diagonals. Find the number of its sides.
The value of `""^50"C"_4 + sum_("r" = 1)^6 ""^(56 - "r")"C"_3` is ______.
All possible numbers are formed using the digits 1, 1, 2, 2, 2, 2, 3, 4, 4 taken all at a time. The number of such numbers in which the odd digits occupy even places is ______.
There are 12 balls numbered from 1 to 12. The number of ways in which they can be used to fill 8 places in a row so that the balls are with numbers in ascending or descending order is equal to ______.
The no. of different ways, the letters of the word KUMARI can be placed in the 8 boxes of the given figure so that no row remains empty will be ______.
The number of words, with or without meaning, that can be formed by taking 4 letters at a time from the letters of the word 'SYLLABUS' such that two letters are distinct and two letters are alike is ______.
A regular polygon has 20 sides. The number of triangles that can be drawn by using the vertices but not using the sides is
