Advertisements
Advertisements
प्रश्न
How many odd numbers less than 1000 can be formed by using the digits 0, 3, 5, 7 when repetition of digits is not allowed?
Advertisements
उत्तर
Since the number is less than 1000, it could be a three-digit, two-digit or single-digit number.
Case I: Three-digit number:
Now, the hundred's place cannot be zero. Thus, it can be filled with three digits, i.e. 3, 5 and 7.
Also, the unit's place cannot be zero. This is because it is an odd number and one digit has already been used to fill the hundred's place.
Thus, the unit's place can be filled by only 2 digits.
Number of ways of filling the ten's digit = 2 (as repetition is not allowed)
Total three-digit numbers that can be formed = `3xx2xx2=12`
Case II: Two-digit number:
Now, the ten's place cannot be zero. Thus, it can be filled with three digits, i.e. 3, 5 and 7.
Also, the unit's place cannot be zero. This is because it is an odd number and one digit has already been used to fill the ten's place,
Thus, the unit's place can be filled by only 2 digits.
Total two-digit numbers that can be formed = `3xx2=6`
Case III: Single-digit number:
It could be 3, 5 and 7.
Total single-digit numbers that can be formed = 3
Hence, required number = 12 + 6 + 3 = 21
APPEARS IN
संबंधित प्रश्न
How many chords can be drawn through 21 points on a circle?
Determine the number of 5 card 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:
(i) exactly 3 girls?
(ii) atleast 3 girls?
(iii) atmost 3 girls?
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?
Compute:
L.C.M. (6!, 7!, 8!)
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?
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}?
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 3-digit numbers are there, with distinct digits, with each digit odd?
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?
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:
35C35
If nC12 = nC5, find the value of n.
If 15Cr : 15Cr − 1 = 11 : 5, find r.
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. 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 committee of 3 persons is to be constituted from a group of 2 men and 3 women. In how many ways can this be done? How many of these committees would consist of 1 man and 2 women?
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?
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 words can be formed by taking 4 letters at a time from the letters of the word 'MORADABAD'?
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?
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?
There are 13 players of cricket, out of which 4 are bowlers. In how many ways a team of eleven be selected from them so as to include at least two bowlers?
The number of ways in which a host lady can invite for a party of 8 out of 12 people of whom two do not want to attend the party together is
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?
If nCr – 1 = 36, nCr = 84 and nCr + 1 = 126, then find rC2.
In an examination, a student has to answer 4 questions out of 5 questions; questions 1 and 2 are however compulsory. Determine the number of ways in which the student can make the choice.
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 ______.
There are 3 books on Mathematics, 4 on Physics and 5 on English. How many different collections can be made such that each collection consists of:
| C1 | C2 |
| (a) One book of each subject; | (i) 3968 |
| (b) At least one book of each subject: | (ii) 60 |
| (c) At least one book of English: | (iii) 3255 |
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 ______.
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 ______.
Total number of 6-digit numbers in which only and all the five digits 1, 3, 5, 7 and 9 appear is ______.
The number of numbers between 2,000 and 5,000 that can be formed with the digits 0, 1, 2, 3, 4, (repetition of digits is not allowed) and are multiple of 3 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
