Advertisements
Advertisements
प्रश्न
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.
Advertisements
उत्तर
Total number of balls = 6 + 5 + 7 = 18
Number of red balls = 6
Number of green balls = 5
Number of blue balls = 7
9 balls are to be drawn, 3 of each Colour,
No. of ways of drawing 3 red balls out of 6 red balls = 6C3
Similarly, No. of ways of drawing 3 green balls out of
5 green balls = 5C3
No. of ways of drawing 3 blue balls out of
7 blue balls = 7C3
∴ Total number of ways = 6C3 × 5C3 × 7C3
= `(6!)/(3!3!) xx (5!)/(3!2!) xx (7!)/(3!4!)`
=`(6xx5xx4xx3!)/(3xx2xx1xx3!)xx(5xx4xx3!)/(3!xx2)xx(7xx6xx5xx4!)/(3xx2xx1xx4!)`
= 20 × 10 × 35
= 7000
APPEARS IN
संबंधित प्रश्न
If nC12 = nC5, find the value of n.
f 24Cx = 24C2x + 3, find x.
In how many ways can a student choose 5 courses out of 9 courses if 2 courses are compulsory for every student?
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. In how many ways can he choose the 7 questions?
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.
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: at least 3 girls?
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?
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 C (n, 12) = C (n, 8), then C (22, n) is equal to
There are 3 wicketkeepers and 5 bowlers among 22 cricket players. A team of 11 players is to be selected so that there is exactly one wicketkeeper and at least 4 bowlers in the team. How many different teams can be formed?
Find the number of ways of dividing 20 objects in three groups of sizes 8, 7, and 5.
Find the value of 15C4
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 one boy and one girl
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.
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!)`.
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 ______.
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 ______.
