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.
Advertisements
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
How many chords can be drawn through 21 points on a circle?
How many words, with or without meaning, each of 2 vowels and 3 consonants can be formed from the letters of the word DAUGHTER?
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?
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?
There are four parcels and five post-offices. In how many different ways can the parcels be sent by registered post?
A letter lock consists of three rings each marked with 10 different letters. In how many ways it is possible to make an unsuccessful attempt to open the lock?
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 each can be formed from the digits 4, 5, 6, 7, 8, 9 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.
If nC10 = nC12, find 23Cn.
If nC4 , nC5 and nC6 are in A.P., then find n.
In how many ways can a student choose 5 courses out of 9 courses if 2 courses are compulsory for every student?
How many different products can be obtained by multiplying two or more of the numbers 3, 5, 7, 11 (without repetition)?
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?
Find the number of (i) diagonals
In how many ways can a team of 3 boys and 3 girls be selected from 5 boys and 4 girls?
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.
Out of 18 points in a plane, no three are in the same straight line except five points which are collinear. How many (i) straight lines
Find the number of ways in which : (a) a selection
Find the number of combinations and permutations of 4 letters taken from the word 'EXAMINATION'.
Write \[\sum^m_{r = 0} \ ^{n + r}{}{C}_r\] in the simplified form.
If 15C3r = 15Cr + 3 , then r is equal to
5C1 + 5C2 + 5C3 + 5C4 +5C5 is equal to
Three persons enter a railway compartment. If there are 5 seats vacant, in how many ways can they take these seats?
If C0 + C1 + C2 + ... + Cn = 256, then 2nC2 is equal to
Among 14 players, 5 are bowlers. In how many ways a team of 11 may be formed with at least 4 bowlers?
Find n and r if `""^"n""P"_"r"` = 720 and `""^"n""C"_("n" - "r")` = 120
There are 20 straight lines in a plane so that no two lines are parallel and no three lines are concurrent. Determine the number of points of intersection.
Ten students are to be selected for a project from a class of 30 students. There are 4 students who want to be together either in the project or not in the project. Find the number of possible selections.
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?
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 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
If nC12 = nC8, then n is equal to ______.
The number of ways in which we can choose a committee from four men and six women so that the committee includes at least two men and exactly twice as many women as men 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.
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 |
The number of positive integers satisfying the inequality `""^(n+1)C_(n-2) - ""^(n+1)C_(n-1) ≤ 100` is ______.
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 ______.
A regular polygon has 20 sides. The number of triangles that can be drawn by using the vertices but not using the sides is
