Advertisements
Advertisements
Question
Ten different letters of alphabet are given. Words with five letters are formed from these given letters. Then the number of words which have atleast one letter repeated is ______.
Options
69,760
30,240
99,748
99,784
Advertisements
Solution
Ten different letters of alphabet are given. Words with five letters are formed from these given letters. Then the number of words which have atleast one letter repeated is 69,760.
Explanation:
Number of 5 letters words (with the condition that a letter can be repeated) = 105 = 1,00,000
Again number of words using 5 different letters is 10P5.
= 1,00,000 – 30,240
= 69,760
APPEARS IN
RELATED QUESTIONS
Is 3! + 4! = 7!?
How many 4-digit numbers are there with no digit 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?
Find r if `""^5P_r = 2^6 P_(r-1)`
Find x in each of the following:
In how many ways can three jobs I, II and III be assigned to three persons A, B and C if one person is assigned only one job and all are capable of doing each job?
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?
Find the number of ways in which 8 distinct toys can be distributed among 5 childrens.
Evaluate each of the following:
8P3
Evaluate each of the following:
6P6
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.
The number of five-digit telephone numbers having at least one of their digits repeated is
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
If the letters of the word KRISNA are arranged in all possible ways and these words are written out as in a dictionary, then the rank of the word KRISNA is
The product of r consecutive positive integers is divisible by
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
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
How many six-digit telephone numbers can be formed if the first two digits are 45 and no digit can appear more than once?
How many numbers lesser than 1000 can be formed using the digits 5, 6, 7, 8, and 9 if no digit is repeated?
If nP4 = 12(nP2), find n.
Find the number of arrangements that can be made out of the letters of the word “ASSASSINATION”.
- In how many ways can 8 identical beads be strung on a necklace?
- In how many ways can 8 boys form a ring?
Determine the number of permutations of the letters of the word SIMPLE if all are taken at a time?
8 women and 6 men are standing in a line. How many arrangements are possible if any individual can stand in any position?
How many ways can the product a2 b3 c4 be expressed without exponents?
A coin is tossed 8 times, how many different sequences of heads and tails are possible?
Choose the correct alternative:
If `""^(("n" + 5))"P"_(("n" + 1)) = ((11("n" - 1))/2)^(("n" + 3))"P"_"n"`, then the value of n are
Choose the correct alternative:
The product of r consecutive positive integers is divisible b
Choose the correct alternative:
If Pr stands for rPr then the sum of the series 1 + P1 + 2P2 + 3P3 + · · · + nPn is
In how many ways can 5 children be arranged in a line such that two particular children of them are never together.
Find the number of different words that can be formed from the letters of the word ‘TRIANGLE’ so that no vowels are together
Five boys and five girls form a line. Find the number of ways of making the seating arrangement under the following condition:
| C1 | C2 |
| (a) Boys and girls alternate: | (i) 5! × 6! |
| (b) No two girls sit together : | (ii) 10! – 5! 6! |
| (c) All the girls sit together | (iii) (5!)2 + (5!)2 |
| (d) All the girls are never together : | (iv) 2! 5! 5! |
8-digit numbers are formed using the digits 1, 1, 2, 2, 2, 3, 4, 4. The number of such numbers in which the odd digits do no occupy odd places is ______.
Number of words from the letters of the words BHARAT in which B and H will never come together is ______.
