Advertisements
Advertisements
प्रश्न
Find r if 11C4 + 11C5 + 12C6 + 13C7 = 14Cr
उत्तर
11C4 + 11C5 + 12C6 + 13C7 = 14Cr
∴ (11C4 + 11C5) + 12C6 + 13C7 = 14Cr ...[nCr + nCr–1 = n+1Cr]
∴ (12C5 + 12C6) + 13C7 = 14Cr
∴ (13C6 + 13C7) = 14Cr
∴ 14C7 = 14Cr
If nCx = nCy, then either x = y or x = n – y
∴ r = 7 or r = 14 – 7 = 7
APPEARS IN
संबंधित प्रश्न
Find the value of `""^80"C"_2`
Find the number of diagonals of an n-shaded polygon. In particular, find the number of diagonals when: n = 10
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 no three points are collinear,
Find the number of triangles formed by joining 12 points if four points are collinear.
A word has 8 consonants and 3 vowels. How many distinct words can be formed if 4 consonants and 12 vowels are chosen?
Find n if `""^"n""C"_8 = ""^"n""C"_12`
Find n, if `""^23"C"_(3"n") = ""^23"C"_(2"n" + 3)`
Find r if `""^11"C"_4 + ""^11"C"_5 + ""^12"C"_6 + ""^13"C"_7 = ""^14"C"_"r"`
Find the differences between the largest values in the following: `""^14"C"_r "and" ""^12"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 n and r if nCr–1 : nCr : nCr+1 = 20 : 35 : 42
If nPr = 1814400 and nCr = 45, find n+4Cr+3
Find the number of ways of selecting a team of 3 boys and 2 girls from 6 boys and 4 girls
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 = 10
Find the number of triangles formed by joining 12 points if four points are collinear
A word has 8 consonants and 3 vowels. How many distinct words can be formed if 4 consonants and 2 vowels are chosen?
Find n if nC8 = nC12
Find n if 23C3n = 23C2n+3
Find n if nCn–2 = 15
Find the differences between the greatest values in the following:
15Cr and 11Cr
There are 3 wicketkeepers and 5 bowlers among 22 cricket players. A team of 11 players is to be selected so that there is exactly one wicketkeeper and at least 4 bowlers in the team. How many different teams can be formed?
Five students are selected from 11. How many ways can these students be selected if two specified students are 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
Select the correct answer from the given alternatives.
The number of ways in which 5 male and 2 female members of a committee can be seated around a round table so that the two females are not seated together is
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:
Find the number of ways of dividing 20 objects in three groups of sizes 8, 7 and 5
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
The maximum value of z = 9x + 11y subject to 3x + 2y ≤ 12, 2x + 3y ≤ 12, x ≥ 0, y ≥ 0 is _______.
If vertices of a parallelogram are respectively (2, 2), (3, 2), (4, 4), and (3, 4), then the angle between diagonals is ______
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 ______.
What is the probability of getting a “FULL HOUSE” in five cards drawn in a poker game from a standard pack of 52-cards?
[A FULL HOUSE consists of 3 cards of the same kind (eg, 3 Kings) and 2 cards of another kind (eg, 2 Aces)]
