Advertisements
Advertisements
प्रश्न
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 ______.
विकल्प
216
600
240
3125
Advertisements
उत्तर
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 216.
Explanation:
We know that a number is divisible by 3 when the sum of its digits is divisible by 3.
If we take the digits 0, 1, 2, 4, 5, then the sum of the digits
= 0 + 1 + 2 + 4 + 5 = 12 which is divisible by 3
So, the 5 digit numbers using the digits 0, 1, 2, 4, and 5
TTh Th H T O
4 4 3 2 1
= 4 × 4 × 3 × 2 × 1
= 96
And if we take the digits 1, 2, 3, 4, 5, then their sum
= 1 + 2 + 3 + 4 + 5
= 15 divisible by 3
So, five-digit numbers can be formed using the digits 1, 2, 3, 4, 5 is 5! ways
= 5 × 4 × 3 × 2 × 1
= 120 ways
Total number of ways = 96 + 120
= 216.
APPEARS IN
संबंधित प्रश्न
Evaluate `(n!)/((n-r)!)` when n = 6, r = 2
How many 3-digit numbers can be formed by using the digits 1 to 9 if no digit is repeated?
Find r if `""^5P_r = 2^6 P_(r-1)`
Find x in each of the following:
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.
In how many ways can three jobs I, II and III be assigned to three persons A, B and C if one person is assigned only one job and all are capable of doing each job?
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?
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?
Evaluate each of the following:
P(6, 4)
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 all possible words that can be formed using the letters of the word 'MATHEMATICS'.
Write the number of numbers that can be formed using all for digits 1, 2, 3, 4 ?
If the letters of the word KRISNA are arranged in all possible ways and these words are written out as in a dictionary, then the rank of the word KRISNA is
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?
Suppose 8 people enter an event in a swimming meet. In how many ways could the gold, silver and bronze prizes be awarded?
Three men have 4 coats, 5 waist coats and 6 caps. In how many ways can they wear them?
A test consists of 10 multiple choice questions. In how many ways can the test be answered if question number n has n + 1 choices?
A student appears in an objective test which contain 5 multiple choice questions. Each question has four choices out of which one correct answer.
How will the answer change if each question may have more than one correct answers?
Find the distinct permutations of the letters of the word MISSISSIPPI?
In how many ways can the letters of the word SUCCESS be arranged so that all Ss are together?
A coin is tossed 8 times, how many different sequences of heads and tails are possible?
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
DANGER
Find the sum of all 4-digit numbers that can be formed using digits 1, 2, 3, 4, and 5 repetitions not allowed?
Find the sum of all 4-digit numbers that can be formed using digits 0, 2, 5, 7, 8 without repetition?
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
The number of different words that can be formed from the letters of the word INTERMEDIATE such that two vowels never come together 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 |
If 1P1 + 2. 2p2 + 3. 3p3 + ....... 15. 15P15 = qPr – s, 0 ≤ s ≤ 1, then q+sCr–s is equal to ______.
If m+nP2 = 90 and m–nP2 = 30, then (m, n) is given by ______.
