Advertisements
Advertisements
Question
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 even?
Advertisements
Solution
The given numbers are 1, 1, 2, 3, 3, 4
| Unit |
In order to get even 6-digit numbers
The unit place must be filled by the digits 2 or 4.
Therefore, the unit place can be filled in 2 ways using the digits 2 or 4.
In the remaining 5 digits (excluding the digit placed in the unit place 2 or 4) 1 occurs 2 times, 3 occurs 2 times.
∴ The number of ways of filling other places using the remaining 5 digit is = `(5!)/(2! xx 2!)`
∴ Number of distinct 6-digit numbers = `(5!)/(2! xx 2!) xx 2`
`(5!)/(2! xx 2!)`
= 5 × 4 × 3
= 60
APPEARS IN
RELATED QUESTIONS
How many words, with or without meaning, can be formed using all the letters of the word EQUATION, using each letter exactly once?
How many three digit numbers can be formed by using the digits 0, 1, 3, 5, 7 while each digit may be repeated any number of times?
Write the number of numbers that can be formed using all for digits 1, 2, 3, 4 ?
The number of permutations of n different things taking r at a time when 3 particular things are to be included is
The number of five-digit telephone numbers having at least one of their digits repeated is
The number of ways in which the letters of the word ARTICLE can be arranged so that even places are always occupied by consonants is
How many numbers lesser than 1000 can be formed using the digits 5, 6, 7, 8, and 9 if no digit is repeated?
Evaluate the following.
`((3!)! xx 2!)/(5!)`
The number of ways to arrange the letters of the word “CHEESE”:
Suppose 8 people enter an event in a swimming meet. In how many ways could the gold, silver and bronze prizes be awarded?
A test consists of 10 multiple choice questions. In how many ways can the test be answered if the first four questions have three choices and the remaining have five choices?
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 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
Choose the correct alternative:
If `""^(("n" + 5))"P"_(("n" + 1)) = ((11("n" - 1))/2)^(("n" + 3))"P"_"n"`, then the value of n are
Find the number of permutations of n different things taken r at a time such that two specific things occur together.
Find the number of permutations of n distinct things taken r together, in which 3 particular things must occur together.
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.
The number of 5-digit telephone numbers having atleast one of their digits repeated is ______.
