हिंदी

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?

Advertisements
Advertisements

प्रश्न

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?

Advertisements

उत्तर

Since the hundred's place cannot be zero, it can be filled by any of the 4 digits (1, 3, 5 and 7).
∴ Number of ways of filling the hundred's place = 4
Since the digits can be repeated in the number, the ten's place and the unit's place can each be filled in 5 ways.
∴ Total numbers = `4xx5xx5=100`

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 16: Permutations - Exercise 16.2 [पृष्ठ १६]

APPEARS IN

आर.डी. शर्मा Mathematics [English] Class 11
अध्याय 16 Permutations
Exercise 16.2 | Q 38 | पृष्ठ १६

वीडियो ट्यूटोरियलVIEW ALL [1]

संबंधित प्रश्न

Is 3! + 4! = 7!?


Compute `(8!)/(6! xx 2!)`


A customer forgets a four-digits code for an Automatic Teller Machine (ATM) in a bank. However, he remembers that this code consists of digits 3, 5, 6 and 9. Find the largest possible number of trials necessary to obtain the correct code.


How many numbers of four digits can be formed with the digits 1, 2, 3, 4, 5 if the digits can be repeated in the same number?


Find the total number of ways in which 20 balls can be put into 5 boxes so that first box contains just one ball ?


In how many ways can 5 different balls be distributed among three boxes?


In how many ways can 7 letters be posted in 4 letter boxes?


There are 10 lamps in a hall. Each one of them can be switched on independently. Find the number of ways in which the hall can be illuminated ?


In how many ways can 4 letters be posted in 5 letter boxes?


Write the number of 5 digit numbers that can be formed using digits 0, 1 and 2 ?


In how many ways 4 women draw water from 4 taps, if no tap remains unused?


Write the number of ways in which 5 boys and 3 girls can be seated in a row so that each girl is between 2 boys ?


The number of different signals which can be given from 6 flags of different colours taking one or more at a time, is


A 5-digit number divisible by 3 is to be formed using the digits 0, 1, 2, 3, 4 and 5 without repetition. The total number of ways in which this can be done is


If k + 5Pk + 1 =\[\frac{11 (k - 1)}{2}\]. k + 3Pk , then the values of k are


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


In how many ways 5 boys and 3 girls can be seated in a row, so that no two girls are together?


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?


  1. In how many ways can 8 identical beads be strung on a necklace?
  2. In how many ways can 8 boys form a ring?

If `""^10"P"_("r" - 1)` = 2 × 6Pr, find r


Suppose 8 people enter an event in a swimming meet. In how many ways could the gold, silver and bronze prizes be awarded?


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. In how many arrangements will no two men be standing next to one another?


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?


How many strings are there using the letters of the word INTERMEDIATE, if all the vowels are together


If the letters of the word GARDEN are permuted in all possible ways and the strings thus formed are arranged in the dictionary order, then find the ranks of the words
GARDEN


Choose the correct alternative:
If `""^(("n" + 5))"P"_(("n" + 1)) = ((11("n" - 1))/2)^(("n" + 3))"P"_"n"`, then the value of n are


The number of arrangements of the letters of the word BANANA in which two N's do not appear adjacently is ______.


In how many ways 3 mathematics books, 4 history books, 3 chemistry books and 2 biology books can be arranged on a shelf so that all books of the same subjects are together.


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 ______.


Find the number of different words that can be formed from the letters of the word ‘TRIANGLE’ so that no vowels are together


In a certain city, all telephone numbers have six digits, the first two digits always being 41 or 42 or 46 or 62 or 64. How many telephone numbers have all six digits distinct?


A five-digit number divisible by 3 is to be formed using the numbers 0, 1, 2, 3, 4 and 5 without repetitions. The total number of ways this can be done is ______.


Using the digits 1, 2, 3, 4, 5, 6, 7, a number of 4 different digits is formed. Find

C1 C2
(a) How many numbers are formed? (i) 840
(b) How many number are exactly divisible by 2? (i) 200
(c) How many numbers are exactly divisible by 25? (iii) 360
(d) How many of these are exactly divisible by 4? (iv) 40

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

If m+nP2 = 90 and m–nP2 = 30, then (m, n) is given by ______.


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 ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×