Advertisements
Advertisements
प्रश्न
There are 3 letters and 3 directed envelopes. Write the number of ways in which no letter is put in the correct envelope.
उत्तर
Total number of ways in which the letters can be put = 3! = 6
Suppose, out of the three letters, one has been put in the correct envelope.
This can be done in 3C1, i.e. 3, ways.
Now, out of three, if two letters have been put in the correct envelope, then the last one has been put in the correct envelope as well.
This can be done in 3C3, i.e. one way.
∴ Number of ways = 3 + 1 = 4
∴ Number of ways in which no letter is put in the correct envelope = 6 - 4 = 2
APPEARS IN
संबंधित प्रश्न
Determine n if `""^(2n)C_3 : ""^nC_3 = 12 : 1`
Find the number of ways of selecting 9 balls from 6 red balls, 5 white balls and 5 blue balls if each selection consists of 3 balls of each colour.
How many 6-digit numbers can be formed from the digits 0, 1, 3, 5, 7 and 9 which are divisible by 10 and no digit is repeated?
Determine the number of 5-card combinations out of a deck of 52 cards if each selection of 5 cards has exactly one king.
From a class of 25 students, 10 are to be chosen for an excursion party. There are 3 students who decide that either all of them will join or none of them will join. In how many ways can the excursion party be chosen?
Given 7 flags of different colours, how many different signals can be generated if a signal requires the use of two flags, one below the other?
How many three-digit numbers are there with no digit repeated?
How many three-digit odd numbers are there?
Since the number has to be greater than 8000, the thousand's place can be filled by only two digits, i.e. 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 = `2xx4xx3xx2=48`
In how many ways can six persons be seated in a row?
If nC4 = nC6, find 12Cn.
f 24Cx = 24C2x + 3, find x.
If 28C2r : 24C2r − 4 = 225 : 11, 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?
How many different selections of 4 books can be made from 10 different books, if
there is no restriction;
How many different selections of 4 books can be made from 10 different books, if
two particular books are always selected;
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. to include at least one officer?
There are 10 points in a plane of which 4 are collinear. How many different straight lines can be drawn by joining these points.
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?
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?
Find the number of ways in which : (a) a selection
How many words can be formed by taking 4 letters at a time from the letters of the word 'MORADABAD'?
Find the number of combinations and permutations of 4 letters taken from the word 'EXAMINATION'.
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?
If C0 + C1 + C2 + ... + Cn = 256, then 2nC2 is equal to
If n + 1C3 = 2 · nC2 , then n =
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.
In how many ways can the letters of the word 'IMAGE' be arranged so that the vowels should always occupy odd places?
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.
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.
15C8 + 15C9 – 15C6 – 15C7 = ______.
The total number of ways in which six ‘+’ and four ‘–’ signs can be arranged in a line such that no two signs ‘–’ occur together is ______.
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.
A scientific committee is to be formed from 6 Indians and 8 foreigners, which includes at least 2 Indians and double the number of foreigners as Indians. Then the number of ways, the committee can be formed is ______.
From 6 different novels and 3 different dictionaries, 4 novels and 1 dictionary are to be selected and arranged in a row on the shelf so that the dictionary is always in the middle. Then, the number of such arrangements is ______.
