हिंदी

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. - Mathematics

Advertisements
Advertisements

प्रश्न

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

उत्तर

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
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 17: Combinations - Exercise 17.4 [पृष्ठ २४]

APPEARS IN

आरडी शर्मा Mathematics [English] Class 11
अध्याय 17 Combinations
Exercise 17.4 | Q 9 | पृष्ठ २४

संबंधित प्रश्न

Convert the following products into factorials:

5 · 6 · 7 · 8 · 9 · 10


Convert the following products into factorials: 

3 · 6 · 9 · 12 · 15 · 18


If (n + 3)! = 56 [(n + 1)!], find n.


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

 

 


Prove that: 

\[\frac{n!}{(n - r)!}\] = n (n − 1) (n − 2) ... (n − (r − 1))

Prove that:

\[\frac{(2n + 1)!}{n!}\] = 2n [1 · 3 · 5 ... (2n − 1) (2n + 1)]

If P(11, r) = P (12, r − 1) find r.


If P (n − 1, 3) : P (n, 4) = 1 : 9, find n.


If P (2n − 1, n) : P (2n + 1, n − 1) = 22 : 7 find n.


From among the 36 teachers in a school, one principal and one vice-principal are to be appointed. In how many ways can this be done?


How many words, with or without meaning, can be formed by using all the letters of the word 'DELHI', using each letter exactly once?


There are 6 items in column A and 6 items in column B. A student is asked to match each item in column A with an item in column B. How many possible, correct or incorrect, answers are there to this question?


How many 6-digit telephone numbers can be constructed with digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 if each number starts with 35 and no digit appears more than once?


If a denotes the number of permutations of (x + 2) things taken all at a time, b the number of permutations of x things taken 11 at a time and c the number of  permutations of x − 11 things taken all at a time such that a = 182 bc, find the value of x.


How many 3-digit even number can be made using the digits 1, 2, 3, 4, 5, 6, 7, if no digits is repeated?


In how many ways can the letters of the word 'FAILURE' be arranged so that the consonants may occupy only odd positions?


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

the vowels never come together? 


How many words can be formed from the letters of the word 'SUNDAY'? How many of these begin with D?


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?


m men and n women are to be seated in a row so that no two women sit together. if m > n then show that the number of ways in which they can be seated as\[\frac{m! (m + 1)!}{(m - n + 1) !}\]


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


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


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


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 different signals can be made from 4 red, 2 white and 3 green flags by arranging all of them vertically on a flagstaff?


How many words can be formed from the letters of the word 'SERIES' which start with S and end with S?


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?


In how many ways can 4 red, 3 yellow and 2 green discs be arranged in a row if the discs of the same colour are indistinguishable?


Prove that: 4nC2n : 2nCn = [1 · 3 · 5 ... (4n − 1)] : [1 · 3 · 5 ... (2n − 1)]2.


Let r and n be positive integers such that 1 ≤ r ≤ n. Then prove the following:

\[\frac{^{n}{}{C}_r}{^{n - 1}{}{C}_{r - 1}} = \frac{n}{r}\]

How many words, with or without meaning can be formed from the letters of the word 'MONDAY', assuming that no letter is repeated, if all letters are used but first letter is a vowel?


If 35Cn +7 = 35C4n − 2 , then write the values of n.


Write the expression nCr +1 + nCr − 1 + 2 × nCr in the simplest form.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×