Advertisements
Advertisements
Question
A box contains two white, three black and four red balls. In how many ways can three balls be drawn from the box, if atleast one black ball is to be included in the draw
Advertisements
Solution
We have 2 white, 3 black and 4 red balls in a box.
3 balls are to be drawn out of 9 balls atleast one black ball is to be included
So, the possible selection is (1 black and 2 other balls)
or (2 black and 1 other ball)
or (3 black and no other ball)
So, the number of possible selection is
= 3C1 × 6C2 + 3C2 × 6C1 + 3C3 × 6C10
= 3 × 15 + 3 ×6 + 1 × 1
= 45 + 18 + 1
= 64
Hence, the required selection = 64.
APPEARS IN
RELATED QUESTIONS
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.
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?
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:
L.C.M. (6!, 7!, 8!)
A coin is tossed five times and outcomes are recorded. How many possible outcomes are there?
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 different five-digit number licence plates can be made if
first digit cannot be zero and the repetition of digits is not allowed,
How many four-digit numbers can be formed with the digits 3, 5, 7, 8, 9 which are greater than 7000, if repetition of digits is not allowed?
How many 3-digit numbers are there, with distinct digits, with each digit odd?
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?
If 18Cx = 18Cx + 2, find x.
If 2nC3 : nC2 = 44 : 3, find n.
From a group of 15 cricket players, a team of 11 players is to be chosen. In how many ways can this be done?
How many different products can be obtained by multiplying two or more of the numbers 3, 5, 7, 11 (without repetition)?
How many different selections of 4 books can be made from 10 different books, if
two particular books are always selected;
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.
Find the number of diagonals of (ii) a polygon of 16 sides.
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?
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?
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(iii) at least 3 girls?
Find the number of (i) diagonals
If 15C3r = 15Cr + 3 , then r is equal to
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
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.
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 ______.
If nC12 = nC8, then n is equal to ______.
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 ______.
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 ______.
If some or all of n objects are taken at a time, the number of combinations is 2n – 1.
The number of positive integers satisfying the inequality `""^(n+1)C_(n-2) - ""^(n+1)C_(n-1) ≤ 100` is ______.
There are (n + 1) white and (n + 1) black balls each set numbered 1 to (n + 1). The number of ways in which the balls can be arranged in row so that the adjacent balls are of different colours 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 ______.
There are ten boys B1, B2, ...., B10 and five girls G1, G2, ...., G5 in a class. Then the number of ways of forming a group consisting of three boys and three girls, if both B1 and B2 together should not be the members of a group is ______.
