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

Answer the following: 30 objects are to be divided in three groups containing 7, 10, 13 objects. Find the number of distinct ways for doing so. - Mathematics and Statistics

Advertisements
Advertisements

प्रश्न

Answer the following:

30 objects are to be divided in three groups containing 7, 10, 13 objects. Find the number of distinct ways for doing so.

बेरीज
Advertisements

उत्तर

Required number = 30C7 × 23C10 × 13C13

= `(30!)/(23!7!) xx (23!)/(10!13!) xx1`

= `(30!)/(7!10!13!)`

shaalaa.com
Properties of Combinations
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 3: Permutations and Combination - Miscellaneous Exercise 3.2 [पृष्ठ ६८]

APPEARS IN

बालभारती Mathematics and Statistics 2 (Arts and Science) [English] Standard 11 Maharashtra State Board
पाठ 3 Permutations and Combination
Miscellaneous Exercise 3.2 | Q II. (8) | पृष्ठ ६८

संबंधित प्रश्‍न

Find the value of 15C4


 Find the value of `""^15"C"_4  + ""^15"C"_5`


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


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


find the value of `sum_("r" = 1)^4  ""^(21 - "r")"C"_4 + ""^17"C"_5`


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?


Five students are selected from 11. How many ways can these students be selected if two specified students are selected?


Nine friends decide to go for a picnic in two groups. One group decides to go by car and the other group decides to go by train. Find the number of different ways of doing so if there must be at least 3 friends in each group.


Find n if nCn–3 = 84


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 diagonals of an n-sided polygon. In particular, find the number of diagonals when n = 10


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


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


Find the number of triangles formed by joining 12 points if no three 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 value of `sum_("r" = 1)^4 ""^((21 - "r"))"C"_4`


Find the differences between the greatest values in the following:

15Cr and 11Cr 


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 majority?


Five students are selected from 11. How many ways can these students be selected if two specified students are selected?


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


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


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


Answer the following:

A student finds 7 books of his interest but can borrow only three books. He wants to borrow the Chemistry part-II book only if Chemistry Part-I can also be borrowed. Find the number of ways he can choose three books that he wants to borrow.


Answer the following:

Find the number of ways of dividing 20 objects in three groups of sizes 8, 7 and 5


Answer the following:

Four parallel lines intersect another set of five parallel lines. Find the number of distinct parallelograms formed


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×