Advertisements
Advertisements
Question
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
Solution
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
RELATED QUESTIONS
Determine n if `""^(2n)C_3 : ""^nC_3 = 12 : 1`
How many chords can be drawn through 21 points on a circle?
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?
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 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?
In how many ways can an examinee answer a set of ten true/false type questions?
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?
A team consists of 6 boys and 4 girls and other has 5 boys and 3 girls. How many single matches can be arranged between the two teams when a boy plays against a boy and a girl plays against a girl?
How many three-digit numbers are there with no digit repeated?
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?
If nC10 = nC12, find 23Cn.
How many different boat parties of 8, consisting of 5 boys and 3 girls, can be made from 25 boys and 10 girls?
In how many ways can a student choose 5 courses out of 9 courses if 2 courses are compulsory for every student?
From 4 officers and 8 jawans in how many ways can 6 be chosen. to include at least one officer?
How many triangles can be obtained by joining 12 points, five of which are collinear?
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 (ii) at least one boy and one girl?
Find the number of (i) diagonals
Find the number of (ii) triangles
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: atmost 3 girls?
Out of 18 points in a plane, no three are in the same straight line except five points which are collinear. How many (i) straight lines
How many different words, each containing 2 vowels and 3 consonants can be formed with 5 vowels and 17 consonants?
If nC12 = nC8 , then n =
5C1 + 5C2 + 5C3 + 5C4 +5C5 is equal to
Three persons enter a railway compartment. If there are 5 seats vacant, in how many ways can they take these seats?
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?
Five students are selected from 11. How many ways can these students be selected if two specified students are not selected?
Find the value of 20C16 – 19C16
A student has to answer 10 questions, choosing atleast 4 from each of Parts A and B. If there are 6 questions in Part A and 7 in Part B, in how many ways can the student choose 10 questions?
A convex polygon has 44 diagonals. Find the number of its sides.
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 at least one boy and one girl
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 total number of ways in which six ‘+’ and four ‘–’ signs can be arranged in a line such that no two signs ‘–’ occur together 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 ______.
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. He can choose the seven questions in 650 ways.
If number of arrangements of letters of the word "DHARAMSHALA" taken all at a time so that no two alike letters appear together is (4a.5b.6c.7d), (where a, b, c, d ∈ N), then a + b + c + d is equal to ______.
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 ______.
