Advertisements
Advertisements
Question
How many numbers lesser than 1000 can be formed using the digits 5, 6, 7, 8, and 9 if no digit is repeated?
Advertisements
Solution
The required numbers are lesser than 1000.
They are one digit, two-digit or three-digit numbers.
There are five numbers to be used without repetition.
One digit number: One-digit numbers are 5.
Two-digit number: 10th place can be filled by anyone of the digits by 5 ways and 1’s place can be 4 filled by any of the remaining four digits in 4 ways.
∴ Two-digit number are 5 × 4 = 20.
Three-digit number: 100th place can be filled by any of the 5 digits, 10th place can be filled by 4 digits and one’s place can be filled by 3 digits.
∴ Three digit numbers are = 5 × 4 × 3 = 60
∴ Total numbers = 5 + 20 + 60 = 85.
APPEARS IN
RELATED QUESTIONS
Evaluate `(n!)/((n-r)!)`, when n = 9, r = 5
Find the number of ways in which one can post 5 letters in 7 letter boxes ?
Evaluate each of the following:
8P3
Evaluate each of the following:
In how many ways 4 women draw water from 4 taps, if no tap remains unused?
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
If the letters of the word FUNNY are permuted in all possible ways and the strings thus formed are arranged in the dictionary order, find the rank of the word FUNNY
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.
If the letters of the word 'MOTHER' be permuted and all the words so formed (with or without meaning) be listed as in a dictionary, then the position of the word 'MOTHER' is ______.
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 ______.
