Advertisements
Advertisements
Question
In how many ways can 4 letters be posted in 5 letter boxes?
Advertisements
Solution
Each of the letter can be posted in anyone of the letter boxes.
This means that every letter can be posted in 5 ways.
∴ Total number of ways of posting 4 letters = `5xx5xx5xx5=5^4`
APPEARS IN
RELATED QUESTIONS
How many 4-digit numbers are there with no digit repeated?
Find r if `""^5P_r = 2^6 P_(r-1)`
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 vowels are all together.
In how many ways can the letters of the word PERMUTATIONS be arranged if the there are always 4 letters between P and S?
In how many ways can the letters of the word ASSASSINATION be arranged so that all the S’s are together?
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?
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?
Write the total number of possible outcomes in a throw of 3 dice in which at least one of the dice shows an even number.
Write the number of words that can be formed out of the letters of the word 'COMMITTEE' ?
Write the number of all possible words that can be formed using the letters of the word 'MATHEMATICS'.
The number of five-digit telephone numbers having at least one of their digits repeated is
The number of words that can be formed out of the letters of the word "ARTICLE" so that vowels occupy even places is
The number of arrangements of the word "DELHI" in which E precedes I is
The number of ways in which the letters of the word 'CONSTANT' can be arranged without changing the relative positions of the vowels and consonants 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
In a room there are 12 bulbs of the same wattage, each having a separate switch. The number of ways to light the room with different amounts of illumination 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?
In how many ways 5 boys and 3 girls can be seated in a row, so that no two girls are together?
- In how many ways can 8 identical beads be strung on a necklace?
- In how many ways can 8 boys form a ring?
Evaluate the following.
`(3! + 1!)/(2^2!)`
The greatest positive integer which divide n(n + 1) (n + 2) (n + 3) for all n ∈ N is:
The number of permutation of n different things taken r at a time, when the repetition is allowed is ______.
Three men have 4 coats, 5 waist coats and 6 caps. In how many ways can they wear them?
8 women and 6 men are standing in a line. How many arrangements are possible if any individual can stand in any position?
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
How many strings are there using the letters of the word INTERMEDIATE, if the vowels and consonants are alternative
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?
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 divisible by 4?
Find the sum of all 4-digit numbers that can be formed using digits 0, 2, 5, 7, 8 without repetition?
In how many ways can 5 children be arranged in a line such that two particular children of them are always together
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)`
Find the number of permutations of n different things taken r at a time such that two specific things occur together.
The number of 5-digit telephone numbers having atleast one of their digits repeated 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 |
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.
If m+nP2 = 90 and m–nP2 = 30, then (m, n) is given by ______.
