Advertisements
Advertisements
Question
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?
Solution
Given that each number starts with 35. We need a 6 digit number. So we have to fill only one’s place, 10’s place, 100th place, and 1000th places. We have to use 10 digits.
In these digits, 3 and 5 should not be used as a repetition of digits is not allowed. Except for these two digits, we have to use 8 digits. One’s place can be filled by any of the 8 digits in different ways, 10’s place can be filled by the remaining 7 digits in 7 different ways.
100th place can be filled by the remaining 6 different ways and 1000th place can be filled by the remaining 5 digits in 5 different ways.
∴ Number of 6 digit telephone numbers = 8 × 7 × 6 × 5 = 1680
APPEARS IN
RELATED QUESTIONS
Find r if `""^5P_r = 2^6 P_(r-1)`
Find x in each of the following:
Find the total number of ways in which 20 balls can be put into 5 boxes so that first box contains just one ball ?
Write the remainder obtained when 1! + 2! + 3! + ... + 200! is divided by 14 ?
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
If (n+2)! = 60[(n–1)!], find n
Three men have 4 coats, 5 waist coats and 6 caps. In how many ways can they wear them?
The number of different words that can be formed from the letters of the word INTERMEDIATE such that two vowels never come together 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.
