Advertisements
Advertisements
प्रश्न
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.
Advertisements
उत्तर
Given that bag contains 5 black and 6 red balls.
Number of ways of selecting 2 black balls out of 5 black balls = 5C2
And number of ways of selecting 3 red balls out of 6 red balls = 6C3
∴ Total number of ways of selecting 2 black and 3 red balls = 5C2 × 6C3
= `(5*4)/(2*1) xx (6*5*4)/(3*2*1)`
= 10 × 20
= 200 ways
Hence, the required ways of selecting the balls = 200.
APPEARS IN
संबंधित प्रश्न
If nC8 = nC2, find nC2.
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?
In a class there are 27 boys and 14 girls. The teacher wants to select 1 boy and 1 girl to represent the class in a function. In how many ways can the teacher make this selection?
A person wants to buy one fountain pen, one ball pen and one pencil from a stationery shop. If there are 10 fountain pen varieties, 12 ball pen varieties and 5 pencil varieties, in how many ways can he select these articles?
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?
Twelve students complete in a race. In how many ways first three prizes be given?
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?
In how many ways can six persons be seated in a row?
A number lock on a suitcase has 3 wheels each labelled with ten digits 0 to 9. If opening of the lock is a particular sequence of three digits with no repeats, how many such sequences will be possible? Also, find the number of unsuccessful attempts to open the lock.
Evaluate the following:
14C3
If 15C3r = 15Cr + 3, find r.
If 8Cr − 7C3 = 7C2, find r.
If 28C2r : 24C2r − 4 = 225 : 11, find r.
From a group of 15 cricket players, a team of 11 players is to be chosen. In how many ways can this be done?
There are 10 professors and 20 students out of whom a committee of 2 professors and 3 students is to be formed. Find the number of ways in which this can be done. Further find in how many of these committees:
a particular professor is included.
How many different selections of 4 books can be made from 10 different books, if
two particular books are always selected;
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?
Find the number of (ii) triangles
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.
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?
How many different words, each containing 2 vowels and 3 consonants can be formed with 5 vowels and 17 consonants?
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 + 1 = 20Cr − 1 , then r is equal to
If C (n, 12) = C (n, 8), then C (22, n) 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 13 players of cricket, out of which 4 are bowlers. In how many ways a team of eleven be selected from them so as to include at least two bowlers?
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
Find n and r if `""^"n""P"_"r"` = 720 and `""^"n""C"_("n" - "r")` = 120
A student finds 7 books of his interest, but can borrow only three books. He wants to borrow Chemistry part II book only if Chemistry Part I can also be borrowed. Find the number of ways he can choose three books that he wants to borrow.
Find the value of 15C4
In how many ways a committee consisting of 3 men and 2 women, can be chosen from 7 men and 5 women?
A convex polygon has 44 diagonals. Find the number of its sides.
There are 12 points in a plane of which 5 points are collinear, then the number of lines obtained by joining these points in pairs is 12C2 – 5C2.
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 ______.
