मराठी
महाराष्ट्र राज्य शिक्षण मंडळएचएससी विज्ञान (सामान्य) इयत्ता ११ वी

Find n if nCn–3 = 84 - Mathematics and Statistics

Advertisements
Advertisements

प्रश्न

Find n if nCn–3 = 84

बेरीज
Advertisements

उत्तर

nCn–3 = 84

∴ `("n"!)/(("n" - 3)!["n" - ("n" - 3)]!)` = 84

∴ `("n"("n" - 1)("n" - 2)("n" - 3)!)/(("n" - 3)! xx 3!)` = 84

∴ n(n – 1)(n – 2) = 84 × 6

∴ n(n – 1)(n – 2) = 9 × 8 × 7

Comparing on both sides, we get n = 9

shaalaa.com
Properties of Combinations
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 3: Permutations and Combination - Exercise 3.6 [पृष्ठ ६४]

APPEARS IN

बालभारती Mathematics and Statistics 2 (Arts and Science) [English] Standard 11 Maharashtra State Board
पाठ 3 Permutations and Combination
Exercise 3.6 | Q 2. (c) | पृष्ठ ६४

संबंधित प्रश्‍न

Find the value of 15C4


Find r if `""^14"C"_(2"r"): ""^10"C"_(2"r" - 4)` = 143:10


Find n and r if `""^"n""C"_("r" - 1): ""^"n""C"_"r": ""^"n""C"_("r" + 1)` = 20:35:42


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 = 10


Find the number of diagonals of an n-shaded polygon. In particular, find the number of diagonals when: n = 15


Find the number of diagonals of an n-shaded polygon. In particular, find the number of diagonals when: n = 12


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,


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 `""^23"C"_(3"n") = ""^23"C"_(2"n" + 3)`


Find n, if `""^21"C"_(6"n") = ""^21"C"_(("n"^2 + 5)`


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`


In how many ways can a boy invite his 5 friends to a party so that at least three join the party?


A group consists of 9 men and 6 women. A team of 6 is to be selected. How many of possible selections will have at least 3 women?


A committee of 10 persons is to be formed from a group of 10 women and 8 men. How many possible committees will have at least 5 women? How many possible committees will have men in the majority?


Find n if 2nC3 : nC2 = 52 : 3


Find n and r if nPr = 720 and nCn–r = 120


If nPr = 1814400 and nCr = 45, find n+4Cr+3 


If nCr–1 = 6435, nCr = 5005, nCr+1 = 3003, find rC5


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


After a meeting, every participant shakes hands with every other participants. If the number of handshakes is 66, find the number of participants in the meeting.


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 n if nC8 = nC12 


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 not selected?


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.


If vertices of a parallelogram are respectively (2, 2), (3, 2), (4, 4), and (3, 4), then the angle between diagonals is ______


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 ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×