Advertisements
Advertisements
प्रश्न
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?
Advertisements
उत्तर
Out of 17 players, 11 need to be selected. There are 5 bowlers, of which four must be selected in the team. So, we have to choose 7 players from the remaining 12 players.
Required number of ways =\[{}^5 C_4 \times^{12} C_7 = 5 \times \frac{12!}{7! 5!} = 5 \times 792 = 3960\]
APPEARS IN
संबंधित प्रश्न
Determine n if `""^(2n)C_3 : ""^nC_3 = 12 : 1`
Determine n if `""^(2n)C_3 : ""^nC_3 = 11: 1`
In how many ways can a team of 3 boys and 3 girls be selected from 5 boys and 4 girls?
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.
How many words, with or without meaning, can be formed using all the letters of the word EQUATION at a time so that the vowels and consonants occur together?
How many A.P.'s with 10 terms are there whose first term is in the set {1, 2, 3} and whose common difference is in the set {1, 2, 3, 4, 5}?
Evaluate the following:
14C3
f 24Cx = 24C2x + 3, find x.
If 18Cx = 18Cx + 2, find x.
If nC4 , nC5 and nC6 are in A.P., then find n.
If 16Cr = 16Cr + 2, find rC4.
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?
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 included.
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?
How many different selections of 4 books can be made from 10 different books, if
two particular books are always selected;
From 4 officers and 8 jawans in how many ways can 6 be chosen (i) to include exactly one officer
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?
In a village, there are 87 families of which 52 families have at most 2 children. In a rural development programme, 20 families are to be helped chosen for assistance, of which at least 18 families must have at most 2 children. In how many ways can the choice be made?
A group consists of 4 girls and 7 boys. In how many ways can a team of 5 members be selected if the team has (i) no girl?
A group consists of 4 girls and 7 boys. In how many ways can a team of 5 members be selected if the team has(iii) at least 3 girls?
We wish to select 6 persons from 8, but if the person A is chosen, then B must be chosen. In how many ways can the selection be made?
How many words can be formed by taking 4 letters at a time from the letters of the word 'MORADABAD'?
If 20Cr + 1 = 20Cr − 1 , then r is equal to
If nC12 = nC8 , then n =
If\[\ ^{( a^2 - a)}{}{C}_2 = \ ^{( a^2 - a)}{}{C}_4\] , then a =
Three persons enter a railway compartment. If there are 5 seats vacant, in how many ways can they take these seats?
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 n + 1C3 = 2 · nC2 , then n =
Find the value of 15C4
If α = mC2, then αC2 is equal to.
In how many ways can the letters of the word 'IMAGE' be arranged so that the vowels should always occupy odd places?
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.
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 must all be of the same colour.
Total number of words formed by 2 vowels and 3 consonants taken from 4 vowels and 5 consonants is equal to ______.
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 ______.
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 ______.
The value of `""^50"C"_4 + sum_("r" = 1)^6 ""^(56 - "r")"C"_3` is ______.
A badminton club has 10 couples as members. They meet to organise a mixed double match. If each wife refers to p artner as well as oppose her husband in the match, then the number of different ways can the match off will be ______.
