English

Write the Number of Ways in Which 5 Red and 4 White Balls Can Be Drawn from a Bag Containing 10 Red and 8 White Balls.

Advertisements
Advertisements

Question

Write the number of ways in which 5 red and 4 white balls can be drawn from a bag containing 10 red and 8 white balls.

Advertisements

Solution

4 white and 5 red balls are to be selected from 8 white and 10 red balls.
∴ Required number of ways =\[{}^8 C_4 \times^{10} C_5\]

shaalaa.com
Factorial N (N!) Permutations and Combinations
  Is there an error in this question or solution?
Chapter 17: Combinations - Exercise 17.4 [Page 24]

APPEARS IN

R.D. Sharma Mathematics [English] Class 11
Chapter 17 Combinations
Exercise 17.4 | Q 9 | Page 24

RELATED QUESTIONS

Convert the following products into factorials: 

3 · 6 · 9 · 12 · 15 · 18


Convert the following products into factorials: 

(n + 1) (n + 2) (n + 3) ... (2n)


Convert the following products into factorials:

1 · 3 · 5 · 7 · 9 ... (2n − 1)


If \[\frac{(2n)!}{3! (2n - 3)!}\]  and \[\frac{n!}{2! (n - 2)!}\]  are in the ratio 44 : 3, find n.

 

 


Prove that:

\[\frac{n!}{(n - r)! r!} + \frac{n!}{(n - r + 1)! (r - 1)!} = \frac{(n + 1)!}{r! (n - r + 1)!}\]


If nP4 = 360, find the value of n.


If P (n, 5) : P (n, 3) = 2 : 1, find n.


If P (15, r − 1) : P (16, r − 2) = 3 : 4, find r.


In how many ways can five children stand in a queue?


Four books, one each in Chemistry, Physics, Biology and Mathematics, are to be arranged in a shelf. In how many ways can this be done?


How many 3-digit numbers can be formed by using the digits 1 to 9 if no digit is repeated?


Find the number of 4-digit numbers that can be formed using the digits 1, 2, 3, 4, 5, if no digit is repeated? How many of these will be even?


In how many ways can the letters of the word 'STRANGE' be arranged so that

the vowels come together?

 


In how many ways can the letters of the word 'STRANGE' be arranged so that

the vowels never come together? 


How many permutations can be formed by the letters of the word, 'VOWELS', when

each word begins with O and ends with L?


How many permutations can be formed by the letters of the word, 'VOWELS', when

all vowels come together?


Find the number of words formed by permuting all the letters of the following words:
INDEPENDENCE


Find the number of words formed by permuting all the letters of the following words:

INDIA


How many words can be formed with the letters of the word 'PARALLEL' so that all L's do not come together?


How many words can be formed by arranging the letters of the word 'MUMBAI' so that all M's come together?


How many numbers can be formed with the digits 1, 2, 3, 4, 3, 2, 1 so that the odd digits always occupy the odd places?


How many number of four digits can be formed with the digits 1, 3, 3, 0?


Find the number of numbers, greater than a million, that can be formed with the digits 2, 3, 0, 3, 4, 2, 3.


How many different arrangements can be made by using all the letters in the word 'MATHEMATICS'. How many of them begin with C? How many of them begin with T?


A biologist studying the genetic code is interested to know the number of possible arrangements of 12 molecules in a chain. The chain contains 4 different molecules represented by the initials A (for Adenine), C (for Cytosine), G (for Guanine) and T (for Thymine) and 3 molecules of each kind. How many different such arrangements are possible?


How many numbers greater than 1000000 can be formed by using the digits 1, 2, 0, 2, 4, 2, 4?


If the permutations of a, b, c, d, e taken all together be written down in alphabetical order as in dictionary and numbered, find the rank of the permutation debac ?


Find the total number of ways in which six ‘+’ and four ‘−’ signs can be arranged in a line such that no two ‘−’ signs occur together.


In how many ways can the letters of the word "INTERMEDIATE" be arranged so that:

the relative order of vowels and consonants do not alter?


The letters of the word 'ZENITH' are written in all possible orders. How many words are possible if all these words are written out as in a dictionary? What is the rank of the word 'ZENITH'?


For all positive integers n, show that 2nCn + 2nCn − 1 = `1/2` 2n + 2Cn+1 


There are 10 persons named\[P_1 , P_2 , P_3 , . . . . , P_{10}\]
Out of 10 persons, 5 persons are to be arranged in a line such that in each arrangement P1 must occur whereas P4 and P5 do not occur. Find the number of such possible arrangements.


Write the maximum number of points of intersection of 8 straight lines in a plane.


Write the number of parallelograms that can be formed from a set of four parallel lines intersecting another set of three parallel lines.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×