Advertisements
Advertisements
प्रश्न
A business man hosts a dinner to 21 guests. He is having 2 round tables which can accommodate 15 and 6 persons each. In how many ways can he arrange the guests?
Advertisements
उत्तर
A businessman hosts a dinner for 21 guests.
15 people can be accommodated at one table in 21C15 ways. They can arrange themselves in \[\left( 15 - 1 \right)! = 14!\]ways.
The remaining 6 people can be accommodated at another table in 6C6 ways. They can arrange themselves in\[\left( 6 - 1 \right)! = 5!\] ways.
∴ Total number of ways =\[{}^{21} C_{15} \times^6 C_6 \times 14! \times 5! =^{21} C_{15} \times 14! \times 5!\]
APPEARS IN
संबंधित प्रश्न
It is required to seat 5 men and 4 women in a row so that the women occupy the even places. How many such arrangements are possible?
A mint prepares metallic calendars specifying months, dates and days in the form of monthly sheets (one plate for each month). How many types of calendars should it prepare to serve for all the possibilities in future years?
A team consists of 6 boys and 4 girls and other has 5 boys and 3 girls. How many single matches can be arranged between the two teams when a boy plays against a boy and a girl plays against a girl?
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 3-digit numbers are there, with distinct digits, with each digit odd?
If 18Cx = 18Cx + 2, find x.
If 15Cr : 15Cr − 1 = 11 : 5, find r.
If 16Cr = 16Cr + 2, find rC4.
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?
From 4 officers and 8 jawans in how many ways can 6 be chosen (i) to include exactly one officer
From 4 officers and 8 jawans in how many ways can 6 be chosen. to include at least one officer?
A student has to answer 10 questions, choosing at least 4 from each of part A and part B. If there are 6 questions in part A and 7 in part B, in how many ways can the student choose 10 questions?
Find the number of diagonals of (ii) a polygon of 16 sides.
In how many ways can a committee of 5 persons be formed out of 6 men and 4 women when at least one woman has to be necessarily selected?
In a village, there are 87 families of which 52 families have at most 2 children. In a rural development programme, 20 families are to be helped chosen for assistance, of which at least 18 families must have at most 2 children. In how many ways can the choice be made?
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 (i) no girl?
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 committee of 7 has to be formed from 9 boys and 4 girls. In how many ways can this be done when the committee consists of: atmost 3 girls?
Write \[\sum^m_{r = 0} \ ^{n + r}{}{C}_r\] in the simplified form.
If 15C3r = 15Cr + 3 , then r is equal to
If nC12 = nC8 , then n =
If nCr + nCr + 1 = n + 1Cx , then x =
Total number of words formed by 2 vowels and 3 consonants taken from 4 vowels and 5 consonants is equal to
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 parallelograms that can be formed from a set of four parallel lines intersecting another set of three parallel lines is
Find n if `""^6"P"_2 = "n" ""^6"C"_2`
There are 3 wicketkeepers and 5 bowlers among 22 cricket players. A team of 11 players is to be selected so that there is exactly one wicketkeeper and at least 4 bowlers in the team. How many different teams can be formed?
Find the value of 20C16 – 19C16
In how many ways can the letters of the word 'IMAGE' be arranged so that the vowels should always occupy odd places?
A boy has 3 library tickets and 8 books of his interest in the library. Of these 8, he does not want to borrow Mathematics Part II, unless Mathematics Part I is also borrowed. In how many ways can he choose the three books to be borrowed?
A bag contains six white marbles and five red marbles. Find the number of ways in which four marbles can be drawn from the bag if they can be of any colour
Total number of words formed by 2 vowels and 3 consonants taken from 4 vowels and 5 consonants is equal to ______.
The number of ways in which we can choose a committee from four men and six women so that the committee includes at least two men and exactly twice as many women as men is ______.
In a football championship, 153 matches were played, Every two teams played one match with each other. The number of teams, participating in the championship is ______.
There are 10 professors and 20 lecturers out of whom a committee of 2 professors and 3 lecturer is to be formed. Find:
| C1 | C2 |
| (a) In how many ways committee: can be formed | (i) 10C2 × 19C3 |
| (b) In how many ways a particular: professor is included | (ii) 10C2 × 19C2 |
| (c) In how many ways a particular: lecturer is included | (iii) 9C1 × 20C3 |
| (d) In how many ways a particular: lecturer is excluded | (iv) 10C2 × 20C3 |
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 ______.
There are (n + 1) white and (n + 1) black balls each set numbered 1 to (n + 1). The number of ways in which the balls can be arranged in row so that the adjacent balls are of different colours is ______.
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 ______.
