Advertisements
Advertisements
प्रश्न
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 ______.
पर्याय
3600
3720
3800
3600
Advertisements
उत्तर
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 3720.
Explanation:
Possible number of choosing 5 different green dyes = 25
Possible number of choosing 4 blue dyes = 24
And possible number of choosing 3 red dyes = 23
If atleast one blue and one green dyes are selected then the total number of selection
= (25 – 1) × (24 – 1) × 23
= 31 × 15 × 8
= 3720
APPEARS IN
संबंधित प्रश्न
How many chords can be drawn through 21 points on a circle?
In how many ways can a team of 3 boys and 3 girls be selected from 5 boys and 4 girls?
In how many ways can one select a cricket team of eleven from 17 players in which only 5 players can bowl if each cricket team of 11 must include exactly 4 bowlers?
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?
Prove that
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?
There are 5 books on Mathematics and 6 books on Physics in a book shop. In how many ways can a students buy : (i) a Mathematics book and a Physics book (ii) either a Mathematics book or a Physics book?
From among the 36 teachers in a college, one principal, one vice-principal and the teacher-incharge are to be appointed. In how many ways can this be done?
How many 3-digit numbers are there, with distinct digits, with each digit odd?
Evaluate the following:
35C35
If nC10 = nC12, find 23Cn.
If 15C3r = 15Cr + 3, find r.
If 28C2r : 24C2r − 4 = 225 : 11, find r.
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 a committee of 5 persons be formed out of 6 men and 4 women when at least one woman has to be necessarily selected?
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 (ii) at least one boy and one girl?
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?
In how many ways can a student choose a programme of 5 courses if 9 courses are available and 2 specific courses are compulsory for every student?
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: exactly 3 girls?
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?
Find the number of ways in which : (a) a selection
Find the number of ways in which : (b) an arrangement, of four letters can be made from the letters of the word 'PROPORTION'.
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?
If C (n, 12) = C (n, 8), then C (22, n) is equal to
5C1 + 5C2 + 5C3 + 5C4 +5C5 is equal to
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 the number of ways of drawing 9 balls from a bag that has 6 red balls, 5 green balls, and 7 blue balls so that 3 balls of every colour are drawn.
Find the number of ways of dividing 20 objects in three groups of sizes 8, 7, and 5.
Find the value of 15C4
Find the value of 15C4 + 15C5
In a small village, there are 87 families, of which 52 families have atmost 2 children. In a rural development programme 20 families are to be chosen for assistance, of which atleast 18 families must have at most 2 children. In how many ways can the choice be made?
The straight lines l1, l2 and l3 are parallel and lie in the same plane. A total numbers of m points are taken on l1; n points on l2, k points on l3. The maximum number of triangles formed with vertices at these points are ______.
A convex polygon has 44 diagonals. Find the number of its sides.
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
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 they must all be of the same colour.
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 ______.
If some or all of n objects are taken at a time, the number of combinations is 2n – 1.
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 |
