Advertisements
Advertisements
Question
Three persons enter a railway compartment. If there are 5 seats vacant, in how many ways can they take these seats?
Options
60
20
15
125
Advertisements
Solution
60
Three persons can take 5 seats in 5C3 ways. Moreover, 3 persons can sit in \[3!\] ways.
∴ Required number of ways =\[{}^5 C_3 \times 3! = 10 \times 6 = 60\]
APPEARS IN
RELATED QUESTIONS
If nC8 = nC2, find nC2.
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.
Determine the number of 5-card combinations out of a deck of 52 cards if each selection of 5 cards has exactly one king.
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?
A coin is tossed five times and outcomes are recorded. How many possible outcomes are there?
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?
How many A.P.'s with 10 terms are there whose first term is in the set {1, 2, 3} and whose common difference is in the set {1, 2, 3, 4, 5}?
If nC10 = nC12, find 23Cn.
If 28C2r : 24C2r − 4 = 225 : 11, find r.
How many different selections of 4 books can be made from 10 different books, if two particular books are never selected?
From 4 officers and 8 jawans in how many ways can 6 be chosen (i) to include exactly one officer
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 (ii) triangles
Determine the number of 5 cards combinations out of a deck of 52 cards if there is exactly one ace in each combination.
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?
How many different words, each containing 2 vowels and 3 consonants can be formed with 5 vowels and 17 consonants?
If 15C3r = 15Cr + 3 , then r is equal to
If nCr + nCr + 1 = n + 1Cx , then x =
The number of diagonals that can be drawn by joining the vertices of an octagon is
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
Find n and r if `""^"n""P"_"r"` = 720 and `""^"n""C"_("n" - "r")` = 120
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 number of ways of dividing 20 objects in three groups of sizes 8, 7, and 5.
Four parallel lines intersect another set of five parallel lines. Find the number of distinct parallelograms that can be formed.
Find the value of 15C4 + 15C5
The value of `(""^9"C"_0 + ""^9"C"_1) + (""^9"C"_1 + ""^9"C"_2) + ... + (""^9"C"_8 + ""^9"C"_9)` is ______
In a small village, there are 87 families, of which 52 families have atmost 2 children. In a rural development programme 20 families are to be chosen for assistance, of which atleast 18 families must have at most 2 children. In how many ways can the choice be made?
In how many ways a committee consisting of 3 men and 2 women, can be chosen from 7 men and 5 women?
In how many ways can a football team of 11 players be selected from 16 players? How many of them will exclude 2 particular players?
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.
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 ______.
Number of selections of at least one letter from the letters of MATHEMATICS, is ______.
