Advertisements
Advertisements
प्रश्न
In how many ways can a team of 3 boys and 3 girls be selected from 5 boys and 4 girls?
Advertisements
उत्तर
A team of 3 boys and 3 girls is to be selected from 5 boys and 4 girls.
3 boys can be selected from 5 boys in `""^5C_3` ways.
3 girls can be selected from 4 girls in `""^4C_3 `ways.
Therefore, by multiplication principle, number of ways in which a team of 3 boys and 3 girls can be selected
= 5C3 x 4C3
= `(5!)/(3!2!) xx (4!)/(3!1!)`
= `(5 xx 4 xx 3!)/(3! xx 2) xx (4 xx 3!)/(3!)`
= 10 x 4 = 40
APPEARS IN
संबंधित प्रश्न
Determine n if `""^(2n)C_3 : ""^nC_3 = 12 : 1`
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?
From a class of 25 students, 10 are to be chosen for an excursion party. There are 3 students who decide that either all of them will join or none of them will join. In how many ways can the excursion party be chosen?
How many three-digit numbers are there with no digit repeated?
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?
In how many ways can six persons be seated in a row?
How many four digit different numbers, greater than 5000 can be formed with the digits 1, 2, 5, 9, 0 when repetition of digits is not allowed?
Evaluate the following:
14C3
Evaluate the following:
If nC4 = nC6, find 12Cn.
f 24Cx = 24C2x + 3, find x.
If 2nC3 : nC2 = 44 : 3, find n.
If α = mC2, then find the value of αC2.
In how many ways can a football team of 11 players be selected from 16 players? How many of these will
exclude 2 particular players?
From 4 officers and 8 jawans in how many ways can 6 be chosen (i) to include exactly one officer
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?
Find the number of diagonals of , 1.a hexagon
In how many ways can a committee of 5 persons be formed out of 6 men and 4 women when at least one woman has to be necessarily selected?
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 at least one of the 5 cards has to be a king?
A parallelogram is cut by two sets of m lines parallel to its sides. Find the number of parallelograms thus formed.
How many different words, each containing 2 vowels and 3 consonants can be formed with 5 vowels and 17 consonants?
Write \[\sum^m_{r = 0} \ ^{n + r}{}{C}_r\] in the simplified form.
If mC1 = nC2 , then
Three persons enter a railway compartment. If there are 5 seats vacant, in how many ways can they take these seats?
In how many ways can a committee of 5 be made out of 6 men and 4 women containing at least one women?
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
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.
In a small village, there are 87 families, of which 52 families have atmost 2 children. In a rural development programme 20 families are to be chosen for assistance, of which atleast 18 families must have at most 2 children. In how many ways can the choice be made?
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.
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 convex polygon has 44 diagonals. Find the number of its sides.
In how many ways can a football team of 11 players be selected from 16 players? How many of them will exclude 2 particular players?
Given 5 different green dyes, four different blue dyes and three different red dyes, the number of combinations of dyes which can be chosen taking at least one green and one blue dye is ______.
If some or all of n objects are taken at a time, the number of combinations is 2n – 1.
There are 10 professors and 20 lecturers out of whom a committee of 2 professors and 3 lecturer is to be formed. Find:
| C1 | C2 |
| (a) In how many ways committee: can be formed | (i) 10C2 × 19C3 |
| (b) In how many ways a particular: professor is included | (ii) 10C2 × 19C2 |
| (c) In how many ways a particular: lecturer is included | (iii) 9C1 × 20C3 |
| (d) In how many ways a particular: lecturer is excluded | (iv) 10C2 × 20C3 |
There are 12 balls numbered from 1 to 12. The number of ways in which they can be used to fill 8 places in a row so that the balls are with numbers in ascending or descending order is equal to ______.
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 ______.
