Advertisements
Advertisements
प्रश्न
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?
Advertisements
उत्तर
It is given that out of 87 families
52 families have at most 2 children
So other 35 families are of other type.
For rural development programme
20 families are to be chosen for assistance, of which at least 18 families must have atmost 2 children.
Thus, the following are the number of possible choices:
52C18 × 35C2 (18 families having atmost 2 children and 2 selected from other type of families)
52C19 × 35C2 (19 families having at most 2 children and 1 selected from other type of families)
52C20 (All selected 20 families having atmost 2 children)
Hence, the total number of possible choices is
52C18 × 35C2 + 52C19 × 35C2 + 35C1 + 52C20
APPEARS IN
संबंधित प्रश्न
If nC8 = nC2, find nC2.
How many chords can be drawn through 21 points on a circle?
If the different permutations of all the letter of the word EXAMINATION are listed as in a dictionary, how many words are there in this list before the first word starting with E?
Determine the number of 5-card combinations out of a deck of 52 cards if each selection of 5 cards has exactly one king.
Compute:
A mint prepares metallic calendars specifying months, dates and days in the form of monthly sheets (one plate for each month). How many types of calendars should it prepare to serve for all the possibilities in future years?
Given 7 flags of different colours, how many different signals can be generated if a signal requires the use of two flags, one below the other?
From among the 36 teachers in a college, one principal, one vice-principal and the teacher-incharge are to be appointed. In how many ways can this be done?
How many three-digit numbers are there with no digit repeated?
How many three-digit numbers are there?
How many different five-digit number licence plates can be made if
first digit cannot be zero and the repetition of digits is not allowed,
How many 9-digit numbers of different digits can be formed?
Evaluate the following:
14C3
f 24Cx = 24C2x + 3, find x.
If 18Cx = 18Cx + 2, find x.
If 8Cr − 7C3 = 7C2, find r.
If 15Cr : 15Cr − 1 = 11 : 5, find r.
In how many ways can a football team of 11 players be selected from 16 players? How many of these will
include 2 particular players?
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
there is no restriction;
Find the number of (ii) triangles
In how many ways can a team of 3 boys and 3 girls be selected from 5 boys and 4 girls?
How many different words, each containing 2 vowels and 3 consonants can be formed with 5 vowels and 17 consonants?
If 20Cr = 20Cr−10, then 18Cr is equal to
If 15C3r = 15Cr + 3 , then r is equal to
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
The value of\[\left( \ ^{7}{}{C}_0 + \ ^{7}{}{C}_1 \right) + \left( \ ^{7}{}{C}_1 + \ ^{7}{}{C}_2 \right) + . . . + \left( \ ^{7}{}{C}_6 + \ ^{7}{}{C}_7 \right)\] is
If n + 1C3 = 2 · nC2 , then n =
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.
Four parallel lines intersect another set of five parallel lines. Find the number of distinct parallelograms that can be formed.
In how many ways can the letters of the word 'IMAGE' be arranged so that the vowels should always occupy odd places?
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 ______.
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.
Everybody in a room shakes hands with everybody else. The total number of handshakes is 66. The total number of persons in the room is ______.
The number of ways in which we can choose a committee from four men and six women so that the committee includes at least two men and exactly twice as many women as men is ______.
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 ______.
Number of selections of at least one letter from the letters of MATHEMATICS, is ______.
