Advertisements
Advertisements
Question
How many distinct 5 digit numbers can be formed using the digits 3, 2, 3, 2, 4, 5
Solution
5 digit numbers are to be formed from 2, 3, 2, 3, 4, 5.
Case I: Numbers formed from 2, 2, 3, 4, 5 OR 2, 3, 3, 4, 5
Number of such numbers = `(5!)/(2!) xx 2`
= 5!
= 120
Case II: Numbers are formed from 2, 2, 3, 3 and any one of 4 or 5
Number of such numbers = `(5!)/(2!2!) xx 2`
= 60
Required number = 120 + 60
= 180
∴ 180 distinct 5 digit numbers can be formed using the digit 3, 2, 3, 2, 4, 5.
APPEARS IN
RELATED QUESTIONS
Find the number of permutations of letters in the following word:
DIVYA
Find the number of permutations of letters in the following word:
SHANTARAM
Find the number of permutations of letters in the following word:
REPRESENT
Find the number of permutations of letters in the following word:
COMBINE
You have 2 identical books on English, 3 identical books on Hindi, and 4 identical books on Mathematics. Find the number of distinct ways of arranging them on a shelf
A coin is tossed 8 times. In how many ways can we obtain 4 heads and 4 tails?
A bag has 5 red, 4 blue, and 4 green marbles. If all are drawn one by one and their colours are recorded, how many different arrangements can be found?
Find the number of different arrangements of letters in the word MAHARASHTRA. How many of these arrangements have letters R and H never together?
Find the number of different arrangements of letters in the word MAHARASHTRA. How many of these arrangements have all vowels together?
How many different words are formed if the letters R is used thrice and letters S and T are used twice each?
Find the number of arrangements of letters in the word MUMBAI so that the letter B is always next to A
Find the number of arrangements of letters in the word CONSTITUTION that begin and end with N
Find the number of different ways of arranging letters in the word ARRANGE. How many of these arrangements do not have the two R’s and two A’s together?
Find the number of distinct numbers formed using the digits 3, 4, 5, 6, 7, 8, 9, so that odd positions are occupied by odd digits
How many different 6-digit numbers can be formed using digits in the number 659942? How many of them are divisible by 4?
Find the number of distinct words formed from letters in the word INDIAN. How many of them have the two N’s together?
Find the number of different ways of arranging letters in the word PLATOON if the two O’s are never together
Find the number of different ways of arranging letters in the word PLATOON if consonants and vowels occupy alternate positions
Answer the following:
How many numbers formed using the digits 3, 2, 0, 4, 3, 2, 3 exceed one million?
Answer the following:
How many quadratic equations can be formed using numbers from 0, 2, 4, 5 as coefficients if a coefficient can be repeated in an equation?
Answer the following:
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 different 9 digit numbers can be formed from the number 112226677 by rearranging its digits so that the odd digits occupy even positions?
Letters in the word HULULULU are rearranged. The probability of all three L being together is ______.
The number of ways of arranging letters of the ‘HAVANA’, so that V and N do not appear together, is ______.
