Advertisements
Advertisements
प्रश्न
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
उत्तर
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
संबंधित प्रश्न
Determine n if `""^(2n)C_3 : ""^nC_3 = 12 : 1`
Determine n if `""^(2n)C_3 : ""^nC_3 = 11: 1`
Compute:
(i)\[\frac{30!}{28!}\]
Prove that
In how many ways can an examinee answer a set of ten true/false type questions?
Twelve students complete in a race. In how many ways first three prizes be given?
How many three-digit odd numbers are there?
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 9-digit numbers of different digits can be formed?
Evaluate the following:
35C35
Evaluate the following:
If 18Cx = 18Cx + 2, find x.
If 28C2r : 24C2r − 4 = 225 : 11, find r.
If 16Cr = 16Cr + 2, find rC4.
If α = mC2, then find the value of αC2.
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 selections of 4 books can be made from 10 different books, if
two particular books are always selected;
Find the number of diagonals of (ii) a polygon of 16 sides.
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 (i) no 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 team of 3 boys and 3 girls be selected from 5 boys and 4 girls?
Determine the number of 5 cards combinations out of a deck of 52 cards if there is exactly one ace in each combination.
In an examination, a question paper consists of 12 questions divided into two parts i.e., Part I and Part II, containing 5 and 7 questions, respectively. A student is required to attempt 8 questions in all, selecting at least 3 from each part. In how many ways can a student select the questions?
If nCr + nCr + 1 = n + 1Cx , then x =
5C1 + 5C2 + 5C3 + 5C4 +5C5 is equal to
Total number of words formed by 2 vowels and 3 consonants taken from 4 vowels and 5 consonants is equal to
In how many ways can a committee of 5 be made out of 6 men and 4 women containing at least one women?
Find the value of 20C16 – 19C16
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?
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 ______.
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 ______.
In a football championship, 153 matches were played, Every two teams played one match with each other. The number of teams, participating in the championship 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 ______.
Eighteen guests are to be seated, half on each side of a long table. Four particular guests desire to sit on one particular side and three others on other side of the table. The number of ways in which the seating arrangements can be made is `(11!)/(5!6!) (9!)(9!)`.
Total number of 6-digit numbers in which only and all the five digits 1, 3, 5, 7 and 9 appear 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 ______.
A regular polygon has 20 sides. The number of triangles that can be drawn by using the vertices but not using the sides is
