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
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 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 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}?
How many 9-digit numbers of different digits can be formed?
f 24Cx = 24C2x + 3, find x.
If 15C3r = 15Cr + 3, find r.
If n +2C8 : n − 2P4 = 57 : 16, find n.
If α = mC2, then find the value of αC2.
How many different boat parties of 8, consisting of 5 boys and 3 girls, can be made from 25 boys and 10 girls?
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?
Find the number of (i) diagonals
Find the number of (ii) triangles
Out of 18 points in a plane, no three are in the same straight line except five points which are collinear. How many (ii) triangles can be formed by joining them?
Find the number of ways in which : (a) a selection
Find the number of ways in which : (b) an arrangement, of four letters can be made from the letters of the word 'PROPORTION'.
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 + 1 = 20Cr − 1 , then r is equal to
If\[\ ^{( a^2 - a)}{}{C}_2 = \ ^{( a^2 - a)}{}{C}_4\] , then a =
If C0 + C1 + C2 + ... + Cn = 256, then 2nC2 is equal to
The number of ways in which a host lady can invite for a party of 8 out of 12 people of whom two do not want to attend the party together is
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
The number of diagonals that can be drawn by joining the vertices of an octagon is
If n + 1C3 = 2 · nC2 , then n =
The number of parallelograms that can be formed from a set of four parallel lines intersecting another set of three parallel lines is
Find n if `""^(2"n")"C"_3: ""^"n""C"_2` = 52:3
Find the value of 15C4 + 15C5
In a small village, there are 87 families, of which 52 families have atmost 2 children. In a rural development programme 20 families are to be chosen for assistance, of which atleast 18 families must have at most 2 children. In how many ways can the choice be made?
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 no girls
Total number of words formed by 2 vowels and 3 consonants taken from 4 vowels and 5 consonants is equal to ______.
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 ______.
To fill 12 vacancies there are 25 candidates of which 5 are from scheduled castes. If 3 of the vacancies are reserved for scheduled caste candidates while the rest are open to all, the number of ways in which the selection can be made is 5C3 × 20C9.
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 ______.
The number of positive integers satisfying the inequality `""^(n+1)C_(n-2) - ""^(n+1)C_(n-1) ≤ 100` is ______.
Number of selections of at least one letter from the letters of MATHEMATICS, is ______.
Total number of 6-digit numbers in which only and all the five digits 1, 3, 5, 7 and 9 appear is ______.
There are ten boys B1, B2, ...., B10 and five girls G1, G2, ...., G5 in a class. Then the number of ways of forming a group consisting of three boys and three girls, if both B1 and B2 together should not be the members of a group 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
