English

Find the Total Number of Ways in Which 20 Balls Can Be Put into 5 Boxes So that First Box Contains Just One Ball ? - Mathematics

Advertisements
Advertisements

Question

Find the total number of ways in which 20 balls can be put into 5 boxes so that first box contains just one ball ?

Solution

Any one of the twenty balls can be put in the first box. Thus, there are twenty different ways for this.
Now, remaining 19 balls are to be put into the remaining 4 boxes. This can be done in`4^19` ways because there are four choices for each ball.
∴ Required number of ways =`20xx4^19`

shaalaa.com
  Is there an error in this question or solution?
Chapter 16: Permutations - Exercise 16.2 [Page 16]

APPEARS IN

RD Sharma Mathematics [English] Class 11
Chapter 16 Permutations
Exercise 16.2 | Q 44 | Page 16

Video TutorialsVIEW ALL [1]

RELATED QUESTIONS

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


How many words, with or without meaning can be made from the letters of the word MONDAY, assuming that no letter is repeated, if

(i) 4 letters are used at a time,

(ii) all letters are used at a time,

(iii) all letters are used but first letter is a vowel?


In how many ways can the letters of the word PERMUTATIONS be arranged if the words start with P and end with S.


Find x in each of the following:

\[\frac{1}{4!} + \frac{1}{5!} = \frac{x}{6!}\]

Find x in each of the following:

\[\frac{x}{10!} = \frac{1}{8!} + \frac{1}{9!}\]

If three six faced die each marked with numbers 1 to 6 on six faces, are thrown find the total number of possible outcomes ?


A coin is tossed three times and the outcomes are recorded. How many possible outcomes are there? How many possible outcomes if the coin is tossed four times? Five times? n times?


How many natural numbers less than 1000 can be formed from the digits 0, 1, 2, 3, 4, 5 when a digit may be repeated any number of times?


How many 5-digit telephone numbers can be constructed using the digits 0 to 9. If each number starts with 67 and no digit appears more than once?


In how many ways can 7 letters be posted in 4 letter boxes?


Evaluate each of the following:

10P

Evaluate each of the following:

6P


Write the number of arrangements of the letters of the word BANANA in which two N's come together.


Write the number of ways in which 6 men and 5 women can dine at a round table if no two women sit together ?


The number of words from the letters of the word 'BHARAT' in which B and H will never come together, is


The number of arrangements of the word "DELHI" in which E precedes I is


Number of all four digit numbers having different digits formed of the digits 1, 2, 3, 4 and 5 and divisible by 4 is


If k + 5Pk + 1 =\[\frac{11 (k - 1)}{2}\]. k + 3Pk , then the values of k are


The number of different ways in which 8 persons can stand in a row so that between two particular persons A and B there are always two persons, is


English alphabet has 11 symmetric letters that appear same when looked at in a mirror. These letters are A, H, I, M, O, T, U, V, W, X and Y. How many symmetric three letters passwords can be formed using these letters?


How many five digits telephone numbers can be constructed using the digits 0 to 9 If each number starts with 67 with no digit appears more than once?


If nP4 = 12(nP2), find n.


  1. In how many ways can 8 identical beads be strung on a necklace?
  2. In how many ways can 8 boys form a ring?

Evaluate the following.

`(3! + 1!)/(2^2!)`


Evaluate the following.

`((3!)! xx 2!)/(5!)`


The greatest positive integer which divide n(n + 1) (n + 2) (n + 3) for all n ∈ N is:


The number of words with or without meaning that can be formed using letters of the word “EQUATION”, with no repetition of letters is:


The number of permutation of n different things taken r at a time, when the repetition is allowed is:


If `""^10"P"_("r" - 1)` = 2 × 6Pr, find r


A student appears in an objective test which contain 5 multiple choice questions. Each question has four choices out of which one correct answer.

What is the maximum number of different answers can the students give?


8 women and 6 men are standing in a line. In how many arrangements will all 6 men be standing next to one another?


A coin is tossed 8 times, how many different sequences of heads and tails are possible?


A coin is tossed 8 times, how many different sequences containing six heads and two tails are possible?


Each of the digits 1, 1, 2, 3, 3 and 4 is written on a separate card. The six cards are then laid out in a row to form a 6-digit number. How many of these 6-digit numbers are even?


In how many ways 3 mathematics books, 4 history books, 3 chemistry books and 2 biology books can be arranged on a shelf so that all books of the same subjects are together.


There are 10 persons named P1, P2, P3, ... P10. 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.


The number of permutations of n different objects, taken r at a line, when repetitions are allowed, is ______.


Using the digits 1, 2, 3, 4, 5, 6, 7, a number of 4 different digits is formed. Find

C1 C2
(a) How many numbers are formed? (i) 840
(b) How many number are exactly divisible by 2? (i) 200
(c) How many numbers are exactly divisible by 25? (iii) 360
(d) How many of these are exactly divisible by 4? (iv) 40

The number of permutations by taking all letters and keeping the vowels of the word ‘COMBINE’ in the odd places is ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×