मराठी

In How Many Ways Can Six Persons Be Seated in a Row?

Advertisements
Advertisements

प्रश्न

In how many ways can six persons be seated in a row?

Advertisements

उत्तर

Number of seats available to the first person = 6
Number of seats available to the second person = 5
Number of seats available to the third person = 4
Number of seats available to the fourth person = 3
Number of seats available to the fifth person = 2
Number of seats available to the sixth person = 1
Total number of ways of making the seating arrangement = `6xx5xx4xx3xx2xx1=720`

shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 16: Permutations - Exercise 16.2 [पृष्ठ १५]

APPEARS IN

आर.डी. शर्मा Mathematics [English] Class 11
पाठ 16 Permutations
Exercise 16.2 | Q 22 | पृष्ठ १५

व्हिडिओ ट्यूटोरियलVIEW ALL [1]

संबंधित प्रश्‍न

In how many ways can a student choose a programme of 5 courses if 9 courses are available and 2 specific courses are compulsory for every student?


If the different permutations of all the letter of the word EXAMINATION are listed as in a dictionary, how many words are there in this list before the first word starting with E?


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?


Compute: 

(i)\[\frac{30!}{28!}\]


Prove that

\[\frac{1}{9!} + \frac{1}{10!} + \frac{1}{11!} = \frac{122}{11!}\]

In a class there are 27 boys and 14 girls. The teacher wants to select 1 boy and 1 girl to represent the class in a function. In how many ways can the teacher make this selection?


There are four parcels and five post-offices. In how many different ways can the parcels be sent by registered post?


How many different five-digit number licence plates can be made if

the first-digit cannot be zero, but the repetition of digits is 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?


Serial numbers for an item produced in a factory are to be made using two letters followed by four digits (0 to 9). If the letters are to be taken from six letters of English alphabet without repetition and the digits are also not repeated in a serial number, how many serial numbers are possible?


A number lock on a suitcase has 3 wheels each labelled with ten digits 0 to 9. If opening of the lock is a particular sequence of three digits with no repeats, how many such sequences will be possible? Also, find the number of unsuccessful attempts to open the lock.


Evaluate the following:

\[\sum^5_{r = 1} {}^5 C_r\]

 


24Cx = 24C2x + 3, find x.


If α = mC2, then find the value of αC2.


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 professor is included.


From 4 officers and 8 jawans in how many ways can 6 be chosen (i) to include exactly one officer


Find the number of (i) diagonals


Determine the number of 5 cards combinations out of a deck of 52 cards if at least one of the 5 cards has to be a king?


In how many ways can a team of 3 boys and 3 girls be selected from 5 boys and 4 girls?


A bag contains 5 black and 6 red balls. Determine the number of ways in which 2 black and 3 red balls can be selected.


Out of 18 points in a plane, no three are in the same straight line except five points which are collinear. How many (ii) triangles can be formed by joining them?


How many words can be formed by taking 4 letters at a time from the letters of the word 'MORADABAD'?


If 15C3r = 15Cr + 3 , then r is equal to


If nC12 = nC8 , then n =


Find the value of 80C2


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?


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?


A box contains two white, three black and four red balls. In how many ways can three balls be drawn from the box, if atleast one black ball is to be included in the draw


If 20 lines are drawn in a plane such that no two of them are parallel and no three are concurrent, in how many points will they intersect each other?


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 ______.


15C8 + 15C915C615C7 = ______.


Three balls are drawn from a bag containing 5 red, 4 white and 3 black balls. The number of ways in which this can be done if at least 2 are red is ______.


A committee of 6 is to be chosen from 10 men and 7 women so as to contain atleast 3 men and 2 women. In how many different ways can this be done if two particular women refuse to serve on the same committee ______.


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.


There are 15 players in a cricket team, out of which 6 are bowlers, 7 are batsmen and 2 are wicketkeepers. The number of ways, a team of 11 players be selected from them so as to include at least 4 bowlers, 5 batsmen and 1 wicketkeeper, is ______.


If number of arrangements of letters of the word "DHARAMSHALA" taken all at a time so that no two alike letters appear together is (4a.5b.6c.7d), (where a, b, c, d ∈ N), then a + b + c + d is equal to ______.


There are 12 persons seated in a line. Number of ways in which 3 persons can be selected such that atleast two of them are consecutive, is ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×