Advertisements
Advertisements
प्रश्न
In how many ways can a committee of 5 be made out of 6 men and 4 women containing at least one women?
विकल्प
246
222
186
none of these
Advertisements
उत्तर
246
\[\text{Required number of ways} =^4 C_1 \times {}^6 C_4 +^4 C_2 \times {}^6 C_3 +^4 C_3 \times {}^6 C_2 +^4 C_4 \times {}^6 C_1 \]
\[ = 60 + 120 + 60 + 6 \]
\[ = 246\]
APPEARS IN
संबंधित प्रश्न
It is required to seat 5 men and 4 women in a row so that the women occupy the even places. How many such arrangements are possible?
Compute:
(i)\[\frac{30!}{28!}\]
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?
In how many ways can six persons be seated in a row?
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:
12C10
Evaluate the following:
n + 1Cn
If 8Cr − 7C3 = 7C2, find r.
If 16Cr = 16Cr + 2, find rC4.
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 excluded.
From a class of 12 boys and 10 girls, 10 students are to be chosen for a competition; at least including 4 boys and 4 girls. The 2 girls who won the prizes last year should be included. In how many ways can the selection be made?
From 4 officers and 8 jawans in how many ways can 6 be chosen. to include at least one officer?
In how many ways can one select a cricket team of eleven from 17 players in which only 5 persons can bowl if each cricket team of 11 must include exactly 4 bowlers?
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?
Find the number of combinations and permutations of 4 letters taken from the word 'EXAMINATION'.
If 20Cr = 20Cr + 4 , then rC3 is equal to
There are 12 points in a plane. The number of the straight lines joining any two of them when 3 of them are collinear, is
How many different committees of 5 can be formed from 6 men and 4 women on which exact 3 men and 2 women serve?
(a) 6
(b) 20
(c) 60
(d) 120
The value of\[\left( \ ^{7}{}{C}_0 + \ ^{7}{}{C}_1 \right) + \left( \ ^{7}{}{C}_1 + \ ^{7}{}{C}_2 \right) + . . . + \left( \ ^{7}{}{C}_6 + \ ^{7}{}{C}_7 \right)\] is
Find n if `""^6"P"_2 = "n" ""^6"C"_2`
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.
If α = mC2, then αC2 is equal to.
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?
How many committee of five persons with a chairperson can be selected from 12 persons.
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.
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 at least three girls.
The number of ways in which a team of eleven players can be selected from 22 players always including 2 of them and excluding 4 of them is ______.
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 ______.
15C8 + 15C9 – 15C6 – 15C7 = ______.
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 ______.
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.
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.
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 ______.
The number of positive integers satisfying the inequality `""^(n+1)C_(n-2) - ""^(n+1)C_(n-1) ≤ 100` is ______.
The number of words, with or without meaning, that can be formed by taking 4 letters at a time from the letters of the word 'SYLLABUS' such that two letters are distinct and two letters are alike is ______.
