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
Determine n if `""^(2n)C_3 : ""^nC_3 = 11: 1`
Prove that
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?
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?
If nC4 , nC5 and nC6 are in A.P., then find n.
How many different products can be obtained by multiplying two or more of the numbers 3, 5, 7, 11 (without repetition)?
From a class of 12 boys and 10 girls, 10 students are to be chosen for a competition; at least including 4 boys and 4 girls. The 2 girls who won the prizes last year should be included. In how many ways can the selection be made?
A sports team of 11 students is to be constituted, choosing at least 5 from class XI and at least 5 from class XII. If there are 20 students in each of these classes, in how many ways can the teams be constituted?
A student has to answer 10 questions, choosing at least 4 from each of part A and part B. If there are 6 questions in part A and 7 in part B, in how many ways can the student choose 10 questions?
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?
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 20Cr = 20Cr + 4 , then rC3 is equal to
If\[\ ^{( a^2 - a)}{}{C}_2 = \ ^{( a^2 - a)}{}{C}_4\] , then a =
There are 12 points in a plane. The number of the straight lines joining any two of them when 3 of them are collinear, is
There are 8 doctors and 4 lawyers in a panel. Find the number of ways for selecting a team of 6 if at least one doctor must be in the team.
There are 10 lamps in a hall. Each one of them can be switched on independently. Find the number of ways in which the hall can be illuminated.
If nCr – 1 = 36, nCr = 84 and nCr + 1 = 126, then find rC2.
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 ______.
