Advertisements
Advertisements
Question
If mC1 = nC2 , then
Options
2 m = n
2 m = n (n + 1)
2 m = n (n − 1)
2 n = m (m − 1)
Advertisements
Solution
2 m = n (n − 1)
mC1 = nC2
\[\Rightarrow \frac{m!}{1! \left( m - 1 \right)!} = \frac{n!}{2! \left( n - 2 \right)!}\]
\[ \Rightarrow \frac{m \left( m - 1 \right)!}{\left( m - 1 \right)!} = \frac{n \left( n - 1 \right) \left( n - 2 \right)!}{2 \left( n - 2 \right)!}\]
\[ \Rightarrow 2m = n \left( n - 1 \right)\]
APPEARS IN
RELATED QUESTIONS
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?
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?
In how many ways can an examinee answer a set of ten true/false type questions?
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?
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 three-digit numbers are there with no digit repeated?
How many three-digit numbers are there?
How many different five-digit number licence plates can be made if
the first-digit cannot be zero, but the repetition of digits is allowed?
In how many ways can six persons be seated in a row?
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?
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.
If nC12 = nC5, find the value of n.
From a group of 15 cricket players, a team of 11 players is to be chosen. In how many ways can this be done?
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?
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 excluded.
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?
There are 10 points in a plane of which 4 are collinear. How many different straight lines can be drawn by joining these points.
How many triangles can be obtained by joining 12 points, five of which are collinear?
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?
In how many ways can a team of 3 boys and 3 girls be selected from 5 boys and 4 girls?
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?
Find the number of ways in which : (b) an arrangement, of four letters can be made from the letters of the word 'PROPORTION'.
If\[\ ^{( a^2 - a)}{}{C}_2 = \ ^{( a^2 - a)}{}{C}_4\] , then a =
Given 11 points, of which 5 lie on one circle, other than these 5, no 4 lie on one circle. Then the number of circles that can be drawn so that each contains at least 3 of the given points is
If n + 1C3 = 2 · nC2 , then n =
Find n if `""^(2"n")"C"_3: ""^"n""C"_2` = 52:3
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 convex polygon has 44 diagonals. Find the number of its sides.
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 two must be white and two red
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?
The number of ways in which a team of eleven players can be selected from 22 players always including 2 of them and excluding 4 of them is ______.
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 ______.
There are 12 points in a plane of which 5 points are collinear, then the number of lines obtained by joining these points in pairs is 12C2 – 5C2.
If some or all of n objects are taken at a time, the number of combinations is 2n – 1.
The value of `""^50"C"_4 + sum_("r" = 1)^6 ""^(56 - "r")"C"_3` is ______.
The number of words, with or without meaning, that can be formed by taking 4 letters at a time from the letters of the word 'SYLLABUS' such that two letters are distinct and two letters are alike is ______.
