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 ?
Advertisements
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`
APPEARS IN
RELATED QUESTIONS
Evaluate 8!
Is 3! + 4! = 7!?
Compute `(8!)/(6! xx 2!)`
How many 3-digit numbers can be formed by using the digits 1 to 9 if no digit is repeated?
From a committee of 8 persons, in how many ways can we choose a chairman and a vice chairman assuming one person cannot hold more than one position?
Find r if `""^5P_r = 2^6 P_(r-1)`
In how many ways can the letters of the word PERMUTATIONS be arranged if the words start with P and end with S.
In how many ways can the letters of the word PERMUTATIONS be arranged if the there are always 4 letters between P and S?
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 numbers of four digits can be formed with the digits 1, 2, 3, 4, 5 if the digits can be repeated in the same number?
Write the number of 5 digit numbers that can be formed using digits 0, 1 and 2 ?
Write the number of words that can be formed out of the letters of the word 'COMMITTEE' ?
The number of six letter words that can be formed using the letters of the word "ASSIST" in which S's alternate with other letters 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
The number of words that can be made by re-arranging the letters of the word APURBA so that vowels and consonants are alternate is
How many numbers lesser than 1000 can be formed using the digits 5, 6, 7, 8, and 9 if no digit is repeated?
How many 6-digit telephone numbers can be constructed with the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 if each numbers starts with 35 and no digit appear more than once?
The number of permutation of n different things taken r at a time, when the repetition is allowed is:
If `""^(("n" – 1))"P"_3 : ""^"n""P"_4` = 1 : 10 find n
A test consists of 10 multiple choice questions. In how many ways can the test be answered if question number n has n + 1 choices?
Find the distinct permutations of the letters of the word MISSISSIPPI?
In how many ways 4 mathematics books, 3 physics books, 2 chemistry books and 1 biology book can be arranged on a shelf so that all books of the same subjects are together
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 distinct 6-digit numbers are there?
If the letters of the word GARDEN are permuted in all possible ways and the strings thus formed are arranged in the dictionary order, then find the ranks of the words
DANGER
Find the number of strings that can be made using all letters of the word THING. If these words are written as in a dictionary, what will be the 85th string?
Find the sum of all 4-digit numbers that can be formed using digits 0, 2, 5, 7, 8 without repetition?
Choose the correct alternative:
If `""^(("n" + 5))"P"_(("n" + 1)) = ((11("n" - 1))/2)^(("n" + 3))"P"_"n"`, then the value of n are
Suppose m men and n women are to be seated in a row so that no two women sit together. If m > n, show that the number of ways in which they can be seated is `(m!(m + 1)!)/((m - n + 1)1)`
In a certain city, all telephone numbers have six digits, the first two digits always being 41 or 42 or 46 or 62 or 64. How many telephone numbers have all six digits distinct?
The number of 5-digit telephone numbers having atleast one of their digits repeated is ______.
How many words (with or without dictionary meaning) can be made from the letters of the word MONDAY, assuming that no letter is repeated, if
| C1 | C2 |
| (a) 4 letters are used at a time | (i) 720 |
| (b) All letters are used at a time | (ii) 240 |
| (c) All letters are used but the first is a vowel | (iii) 360 |
Ten different letters of an alphabet are given. Words with five letters are formed from these given letters. Determine the number of words which have at least one letter repeated.
The number of permutations by taking all letters and keeping the vowels of the word ‘COMBINE’ in the odd places is ______.
