Advertisements
Advertisements
प्रश्न
A box contains 2 white balls, 3 black balls and 4 red balls. The number of ways three balls be drawn from the box if at least one black ball is to be included in the draw is ______.
Advertisements
उत्तर
A box contains 2 white balls, 3 black balls and 4 red balls. The number of ways three balls be drawn from the box if at least one black ball is to be included in the draw is 64.
Explanation:
We have 2 white, 3 black and 4 red balls
It is given that atleast 1 black ball is to be included.
∴ Required number of ways = 3C1 × 6C2 + 3C2 × 6C1 + 3C3
= 3 × 15 + 3 × 6 + 1
= 45 + 18 + 1
= 64
Hence, the value of the filler is 64.
APPEARS IN
संबंधित प्रश्न
Determine n if `""^(2n)C_3 : ""^nC_3 = 12 : 1`
How many chords can be drawn through 21 points on a circle?
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.
The English alphabet has 5 vowels and 21 consonants. How many words with two different vowels and 2 different consonants can be formed from the alphabet?
Compute:
(i)\[\frac{30!}{28!}\]
Compute:
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?
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?
A team consists of 6 boys and 4 girls and other has 5 boys and 3 girls. How many single matches can be arranged between the two teams when a boy plays against a boy and a girl plays against a girl?
Twelve students complete in a race. In how many ways first three prizes be given?
How many three-digit numbers are there with no digit repeated?
How many three-digit odd numbers are there?
In how many ways can six persons be seated in a row?
How many odd numbers less than 1000 can be formed by using the digits 0, 3, 5, 7 when repetition of digits is not allowed?
Evaluate the following:
12C10
Evaluate the following:
35C35
If nC10 = nC12, find 23Cn.
If 2nC3 : nC2 = 44 : 3, find n.
How many different selections of 4 books can be made from 10 different books, if
there is no restriction;
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 tea party is arranged for 16 persons along two sides of a long table with 8 chairs on each side. Four persons wish to sit on one particular side and two on the other side. In how many ways can they be seated?
If 20Cr = 20Cr + 4 , then rC3 is equal to
If nCr + nCr + 1 = n + 1Cx , then x =
If C0 + C1 + C2 + ... + Cn = 256, then 2nC2 is equal to
Given 11 points, of which 5 lie on one circle, other than these 5, no 4 lie on one circle. Then the number of circles that can be drawn so that each contains at least 3 of the given points is
The number of parallelograms that can be formed from a set of four parallel lines intersecting another set of three parallel lines is
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.
Find the number of ways of dividing 20 objects in three groups of sizes 8, 7, and 5.
Find the value of 15C4 + 15C5
All the letters of the word ‘EAMCOT’ are arranged in different possible ways. The number of such arrangements in which no two vowels are adjacent to each other is ______.
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 convex polygon has 44 diagonals. Find the number of its sides.
Everybody in a room shakes hands with everybody else. The total number of handshakes is 66. The total number of persons in the room is ______.
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 ______.
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 ______.
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 ______.
