Advertisements
Advertisements
Question
Find n if nCn–2 = 15
Advertisements
Solution
nCn–2 = 15
∴ nC2 = 15 ...[∵ nCr = nCn–r]
∴ `("n"!)/(("n" - 2)!2!)` = 15
∴ `("n"("n" - 1)("n" - 2)!)/(("n" - 2)!2 xx 1)` = 15
∴ n(n – 1) = 30
∴ n(n – 1) = 6 × 5
Equating both sides, we get
∴ n = 6
APPEARS IN
RELATED QUESTIONS
Find the value of `""^20"C"_16 - ""^19"C"_16`
Find n if `""^"n""C"_("n" - 3)` = 84
If `""^"n""P"_"r" = 1814400` and `""^"n""C"_"r"` = 45, find r.
If 20 points are marked on a circle, how many chords can be drawn?
Find the number of diagonals of an n-shaded polygon. In particular, find the number of diagonals when: n = 15
Ten points are plotted on a plane. Find the number of straight lines obtained by joining these points if no three points are collinear.
Ten points are plotted on a plane. Find the number of straight lines obtained by joining these points if four points are collinear.
Find n, if `""^"n""C"_("n" - 2)` = 15
Find x if `""^"n""P"_"r" = "x" ""^"n""C"_"r"`
Find the differences between the largest values in the following: `""^15"C"_r "and" ""^11"C"_r`
Five students are selected from 11. How many ways can these students be selected if two specified students are selected?
Find n and r if nPr = 720 and nCn–r = 120
Find the number of ways of drawing 9 balls from a bag that has 6 red balls, 8 green balls, and 7 blue balls so that 3 balls of every colour are drawn
If 20 points are marked on a circle, how many chords can be drawn?
Find the number of diagonals of an n-sided polygon. In particular, find the number of diagonals when n = 12
Find the number of diagonals of an n-sided polygon. In particular, find the number of diagonals when n = 8
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
Ten points are plotted on a plane. Find the number of straight lines obtained by joining these points if no three points are collinear
Ten points are plotted on a plane. Find the number of straight lines obtained by joining these points if four points are collinear
Find the number of triangles formed by joining 12 points if four points are collinear
Find n if nC8 = nC12
Find n if 21C6n = `""^21"C"_(("n"^2 + 5))`
Find n if 2nCr–1 = 2nCr+1
Find r if 11C4 + 11C5 + 12C6 + 13C7 = 14Cr
Find the differences between the greatest values in the following:
14Cr and 12Cr
Find the differences between the greatest values in the following:
13Cr and 8Cr
Find the differences between the greatest values in the following:
15Cr and 11Cr
In how many ways can a boy invite his 5 friends to a party so that at least three join the party?
Five students are selected from 11. How many ways can these students be selected if two specified students are not selected?
Select the correct answer from the given alternatives.
The number of arrangements of the letters of the word BANANA in which two N's do not appear adjacently
Answer the following:
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 student passes an examination if he secures a minimum in each of the 7 subjects. Find the number of ways a student can fail.
Answer the following:
There are 4 doctors and 8 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
If `1/(8!) + 1/(7!) = x/(9!)`, than x is equal to ______.
In how many ways can a group of 5 boys and 6 girls be formed out of 10 boys and 11 girls?
If 'n' is positive integer and three consecutive coefficient in the expansion of (1 + x)n are in the ratio 6 : 33 : 110, then n is equal to ______.
Out of 7 consonants and 4 vowels, the number of words (not necessarily meaningful) that can be made, each consisting of 3 consonants and 2 vowels, is ______.
