Advertisements
Advertisements
Question
Find the value of 15C4
Advertisements
Solution
15C4 = `(15!)/(4!(15 - 4)!)`
= `(15!)/(4!11!)`
= `(15 xx 14 xx 13 xx 12 xx 11!)/(4 xx 3 xx 2 xx 1 xx 11!)`
= `(15 xx 14 xx 13 xx 12)/(4 xx 3 xx 2 xx 1)`
= 1365
APPEARS IN
RELATED QUESTIONS
Determine the number of 5 card combinations out of a deck of 52 cards if there is exactly one ace in each combination.
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, each of 2 vowels and 3 consonants can be formed from the letters of the word DAUGHTER?
Determine the number of 5-card combinations out of a deck of 52 cards if each selection of 5 cards has exactly one king.
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?
A person wants to buy one fountain pen, one ball pen and one pencil from a stationery shop. If there are 10 fountain pen varieties, 12 ball pen varieties and 5 pencil varieties, in how many ways can he select these articles?
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 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?
A number lock on a suitcase has 3 wheels each labelled with ten digits 0 to 9. If opening of the lock is a particular sequence of three digits with no repeats, how many such sequences will be possible? Also, find the number of unsuccessful attempts to open the lock.
Evaluate the following:
35C35
If 15C3r = 15Cr + 3, find r.
If 8Cr − 7C3 = 7C2, find r.
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
include 2 particular players?
From 4 officers and 8 jawans in how many ways can 6 be chosen (i) to include exactly one officer
From 4 officers and 8 jawans in how many ways can 6 be chosen. to include at least one officer?
In an examination, a student has to answer 4 questions out of 5 questions; questions 1 and 2 are however compulsory. Determine the number of ways in which the student can make the choice.
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?
Find the number of (i) diagonals
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 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: at least 3 girls?
How many words can be formed by taking 4 letters at a time from the letters of the word 'MORADABAD'?
A business man hosts a dinner to 21 guests. He is having 2 round tables which can accommodate 15 and 6 persons each. In how many ways can he arrange the guests?
If 20Cr = 20Cr−10, then 18Cr is equal to
If 15C3r = 15Cr + 3 , then r is equal to
In how many ways can a committee of 5 be made out of 6 men and 4 women containing at least one women?
If C0 + C1 + C2 + ... + Cn = 256, then 2nC2 is equal to
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.
There are 8 doctors and 4 lawyers in a panel. Find the number of ways for selecting a team of 6 if at least one doctor must be in the team.
Four parallel lines intersect another set of five parallel lines. Find the number of distinct parallelograms that can be formed.
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?
A convex polygon has 44 diagonals. Find the number of its sides.
In how many ways can a football team of 11 players be selected from 16 players? How many of them will include 2 particular players?
Given 5 different green dyes, four different blue dyes and three different red dyes, the number of combinations of dyes which can be chosen taking at least one green and one blue dye is ______.
Eighteen guests are to be seated, half on each side of a long table. Four particular guests desire to sit on one particular side and three others on other side of the table. The number of ways in which the seating arrangements can be made is `(11!)/(5!6!) (9!)(9!)`.
There are 15 players in a cricket team, out of which 6 are bowlers, 7 are batsmen and 2 are wicketkeepers. The number of ways, a team of 11 players be selected from them so as to include at least 4 bowlers, 5 batsmen and 1 wicketkeeper, is ______.
A regular polygon has 20 sides. The number of triangles that can be drawn by using the vertices but not using the sides is
