Advertisements
Advertisements
प्रश्न
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?
Advertisements
उत्तर
Two girls who won the prizes last year are to be included in every selection.
So, we have to select 8 students out of 12 boys and 8 girls, choosing at least 4 boys and 2 girls.
Number of ways in which it can be done =\[{}^{12} C_6 \times^8 C_2 + {}^{12} C_5 \times^8 C_3 + {}^{12} C_4 \times^8 C_4 = 25872 + 44352 + 34650 = 104874\]
APPEARS IN
संबंधित प्रश्न
In how many ways can a team of 3 boys and 3 girls be selected from 5 boys and 4 girls?
Find the number of ways of selecting 9 balls from 6 red balls, 5 white balls and 5 blue balls if each selection consists of 3 balls of each colour.
In how many ways can a student choose a programme of 5 courses if 9 courses are available and 2 specific courses are compulsory for every student?
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:
(i) exactly 3 girls?
(ii) atleast 3 girls?
(iii) atmost 3 girls?
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?
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?
Compute:
(i)\[\frac{30!}{28!}\]
A coin is tossed five times and outcomes are recorded. How many possible outcomes are there?
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?
How many 9-digit numbers of different digits can be formed?
How many odd numbers less than 1000 can be formed by using the digits 0, 3, 5, 7 when repetition of digits is not allowed?
How many 3-digit numbers are there, with distinct digits, with each digit odd?
How many different numbers of six digits each can be formed from the digits 4, 5, 6, 7, 8, 9 when repetition of digits is not allowed?
How many different numbers of six digits can be formed from the digits 3, 1, 7, 0, 9, 5 when repetition of digits is not allowed?
If 15C3r = 15Cr + 3, find r.
If α = mC2, then find the value of αC2.
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 student is excluded.
From 4 officers and 8 jawans in how many ways can 6 be chosen. to include at least one officer?
Find the number of (i) diagonals
Determine the number of 5 cards combinations out of a deck of 52 cards if there is exactly one ace in each combination.
In how many ways can one select a cricket team of eleven from 17 players in which only 5 persons can bowl if each cricket team of 11 must include exactly 4 bowlers?
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?
Find the number of ways in which : (a) a selection
If nC12 = nC8 , then n =
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
If 43Cr − 6 = 43C3r + 1 , then the value of r is
Find n and r if `""^"n""P"_"r"` = 720 and `""^"n""C"_("n" - "r")` = 120
Ten students are to be selected for a project from a class of 30 students. There are 4 students who want to be together either in the project or not in the project. Find the number of possible selections.
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.
A bag contains six white marbles and five red marbles. Find the number of ways in which four marbles can be drawn from the bag if they can be of any colour
Total number of words formed by 2 vowels and 3 consonants taken from 4 vowels and 5 consonants is equal to ______.
The total number of ways in which six ‘+’ and four ‘–’ signs can be arranged in a line such that no two signs ‘–’ occur together is ______.
To fill 12 vacancies there are 25 candidates of which 5 are from scheduled castes. If 3 of the vacancies are reserved for scheduled caste candidates while the rest are open to all, the number of ways in which the selection can be made is 5C3 × 20C9.
There are 3 books on Mathematics, 4 on Physics and 5 on English. How many different collections can be made such that each collection consists of:
| C1 | C2 |
| (a) One book of each subject; | (i) 3968 |
| (b) At least one book of each subject: | (ii) 60 |
| (c) At least one book of English: | (iii) 3255 |
A scientific committee is to be formed from 6 Indians and 8 foreigners, which includes at least 2 Indians and double the number of foreigners as Indians. Then the number of ways, the committee can be formed is ______.
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 ______.
