Advertisements
Advertisements
Question
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?
Advertisements
Solution
Since the number has to be greater than 7000, the thousand's place can only be filled by three digits, i.e. 7, 8 and 9.
Now, the hundred's place can be filled with the remaining 4 digits as the repetition of the digits is not allowed.
The ten's place can be filled with the remaining 3 digits.
The unit's place can be filled with the remaining 2 digits.
Total numbers that can be formed = 3\[\times\]4\[\times\]3\[\times\]2 = 72
APPEARS IN
RELATED QUESTIONS
Determine n if `""^(2n)C_3 : ""^nC_3 = 11: 1`
Compute:
A person wants to buy one fountain pen, one ball pen and one pencil from a stationery shop. If there are 10 fountain pen varieties, 12 ball pen varieties and 5 pencil varieties, in how many ways can he select these articles?
Evaluate the following:
n + 1Cn
Evaluate the following:
f 24Cx = 24C2x + 3, find x.
If n +2C8 : n − 2P4 = 57 : 16, find n.
If 28C2r : 24C2r − 4 = 225 : 11, find r.
If nC4 , nC5 and nC6 are in A.P., then find n.
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?
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 included.
How many different selections of 4 books can be made from 10 different books, if
two particular books are always selected;
From 4 officers and 8 jawans in how many ways can 6 be chosen. to include at least one officer?
A sports team of 11 students is to be constituted, choosing at least 5 from class XI and at least 5 from class XII. If there are 20 students in each of these classes, in how many ways can the teams be constituted?
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?
There are 10 points in a plane of which 4 are collinear. How many different straight lines can be drawn by joining these points.
How many triangles can be obtained by joining 12 points, five of which are collinear?
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(iii) at least 3 girls?
There are 3 letters and 3 directed envelopes. Write the number of ways in which no letter is put in the correct envelope.
If C (n, 12) = C (n, 8), then C (22, n) is equal to
Total number of words formed by 2 vowels and 3 consonants taken from 4 vowels and 5 consonants is equal to
Find n if `""^(2"n")"C"_3: ""^"n""C"_2` = 52:3
A student finds 7 books of his interest, but can borrow only three books. He wants to borrow Chemistry part II book only if Chemistry Part I can also be borrowed. Find the number of ways he can choose three books that he wants to borrow.
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?
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?
All the letters of the word ‘EAMCOT’ are arranged in different possible ways. The number of such arrangements in which no two vowels are adjacent to each other is ______.
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 from the lot.
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 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 two must be white and two red
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 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 ______.
There are 12 points in a plane of which 5 points are collinear, then the number of lines obtained by joining these points in pairs is 12C2 – 5C2.
Number of selections of at least one letter from the letters of MATHEMATICS, is ______.
A badminton club has 10 couples as members. They meet to organise a mixed double match. If each wife refers to p artner as well as oppose her husband in the match, then the number of different ways can the match off will be ______.
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 ______.
A regular polygon has 20 sides. The number of triangles that can be drawn by using the vertices but not using the sides is
