Advertisements
Advertisements
Question
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?
Advertisements
Solution
If 2 particular players are excluded, it would mean that out of 14 players, 11 players are selected. Required number of ways =\[{}^{14} C_{11} = \frac{14!}{11! 3!} = \frac{14 \times 13 \times 12}{3 \times 2 \times 1} = 364\]
APPEARS IN
RELATED QUESTIONS
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?
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?
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?
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?
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 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:
35C35
If 28C2r : 24C2r − 4 = 225 : 11, find r.
If nC4 , nC5 and nC6 are in A.P., then find n.
If α = mC2, then find the value of αC2.
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;
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?
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?
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.
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: exactly 3 girls?
A parallelogram is cut by two sets of m lines parallel to its sides. Find the number of parallelograms thus formed.
Find the number of ways in which : (a) a selection
Find the number of combinations and permutations of 4 letters taken from the word 'EXAMINATION'.
If nC12 = nC8 , then n =
Three persons enter a railway compartment. If there are 5 seats vacant, in how many ways can they take these seats?
Find n if `""^(2"n")"C"_3: ""^"n""C"_2` = 52:3
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.
The value of `(""^9"C"_0 + ""^9"C"_1) + (""^9"C"_1 + ""^9"C"_2) + ... + (""^9"C"_8 + ""^9"C"_9)` is ______
All the letters of the word ‘EAMCOT’ are arranged in different possible ways. The number of such arrangements in which no two vowels are adjacent to each other is ______.
How many committee of five persons with a chairperson can be selected from 12 persons.
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.
If 20 lines are drawn in a plane such that no two of them are parallel and no three are concurrent, in how many points will they intersect each other?
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 ______.
In a football championship, 153 matches were played, Every two teams played one match with each other. The number of teams, participating in the championship 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.
The value of `""^50"C"_4 + sum_("r" = 1)^6 ""^(56 - "r")"C"_3` is ______.
All possible numbers are formed using the digits 1, 1, 2, 2, 2, 2, 3, 4, 4 taken all at a time. The number of such numbers in which the odd digits occupy even places is ______.
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 ______.
The number of numbers between 2,000 and 5,000 that can be formed with the digits 0, 1, 2, 3, 4, (repetition of digits is not allowed) and are multiple of 3 is?
