Advertisements
Advertisements
प्रश्न
How many numbers of six digits can be formed from the digits 0, 1, 3, 5, 7 and 9 when no digit is repeated? How many of them are divisible by 10 ?
Advertisements
उत्तर
The first digit of the number cannot be zero. Thus, it can be filled in 5 ways.
The number of ways of filling the second digit = 5
(as the repetition of digits is not allowed)
The number of ways of filling the third digit = 4
The number of ways of filling the fourth digit = 3
The number of ways of filling the fifth digit = 2
The number of ways of filling the sixth digit = 1
∴ Required numbers =`5xx5xx4xx3xx2xx1=600`
For the number to be divisible by 10, the sixth digit has to be zero.
Now, the first digit can be filled in 5 ways.
Number of ways of filling the second digit = 4
Number of ways of filling the third digit = 3
Number of ways of filling the fourth digit = 2
Number of ways of filling the fifth digit = 1
Number of ways of filling the sixth digit = 1
Total numbers divisible by 10 =`5xx4xx3xx2xx1xx1=120`
APPEARS IN
संबंधित प्रश्न
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:
Find x in each of the following:
Which of the following are true:
(2 +3)! = 2! + 3!
Which of the following are true:
(2 × 3)! = 2! × 3!
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.
A coin is tossed three times and the outcomes are recorded. How many possible outcomes are there? How many possible outcomes if the coin is tossed four times? Five times? n times?
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?
How many natural numbers less than 1000 can be formed from the digits 0, 1, 2, 3, 4, 5 when a digit may be repeated any number of times?
Three dice are rolled. Find the number of possible outcomes in which at least one die shows 5 ?
In how many ways can 4 prizes be distributed among 5 students, when
(i) no student gets more than one prize?
(ii) a student may get any number of prizes?
(iii) no student gets all the prizes?
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 ?
The number of ways to arrange the letters of the word CHEESE are
If k + 5Pk + 1 =\[\frac{11 (k - 1)}{2}\]. k + 3Pk , then the values of k are
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
English alphabet has 11 symmetric letters that appear same when looked at in a mirror. These letters are A, H, I, M, O, T, U, V, W, X and Y. How many symmetric three letters passwords can be formed using these letters?
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?
- In how many ways can 8 identical beads be strung on a necklace?
- In how many ways can 8 boys form a ring?
Evaluate the following.
`(3! xx 0! + 0!)/(2!)`
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?
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?
Choose the correct alternative:
If `""^(("n" + 5))"P"_(("n" + 1)) = ((11("n" - 1))/2)^(("n" + 3))"P"_"n"`, then the value of n are
Choose the correct alternative:
If Pr stands for rPr then the sum of the series 1 + P1 + 2P2 + 3P3 + · · · + nPn is
The number of arrangements of the letters of the word BANANA in which two N's do not appear adjacently is ______.
How many words can be formed with the letters of the word MANAGEMENT by rearranging them?
If all permutations of the letters of the word AGAIN are arranged in the order as in a dictionary. What is the 49th word?
Suppose m men and n women are to be seated in a row so that no two women sit together. If m > n, show that the number of ways in which they can be seated is `(m!(m + 1)!)/((m - n + 1)1)`
Find the number of permutations of n distinct things taken r together, in which 3 particular things must occur 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 ______.
In the permutations of n things, r taken together, the number of permutations in which m particular things occur together is `""^(n - m)"P"_(r - m) xx ""^r"P"_m`.
If 1P1 + 2. 2p2 + 3. 3p3 + ....... 15. 15P15 = qPr – s, 0 ≤ s ≤ 1, then q+sCr–s is equal to ______.
If the letters of the word 'MOTHER' be permuted and all the words so formed (with or without meaning) be listed as in a dictionary, then the position of the word 'MOTHER' is ______.
Number of words from the letters of the words BHARAT in which B and H will never come together is ______.
