Advertisements
Advertisements
प्रश्न
Three dice are rolled. Find the number of possible outcomes in which at least one die shows 5 ?
Advertisements
उत्तर
Required number of possible outcomes = (Total number of outcomes - Number of possible outcomes in which 5 does not appear on any of the dice.)
Total number of outcomes when a single dice is rolled = 6
∴ Total number of outcomes when two dice are rolled =`6xx6`
Similarly, total number of outcomes when three dice are rolled =`6xx6xx6=216`
Number of possible outcomes in which 5 does not appear on any dice =`5xx5xx5=125`
∴ Required number of possible outcomes =`216-125=91`
APPEARS IN
संबंधित प्रश्न
Compute `(8!)/(6! xx 2!)`
Find the number of 4-digit numbers that can be formed using the digits 1, 2, 3, 4, 5 if no digit is repeated. How many of these will be even?
How many words, with or without meaning can be made from the letters of the word MONDAY, assuming that no letter is repeated, if
(i) 4 letters are used at a time,
(ii) all letters are used at a time,
(iii) all letters are used but first letter is a vowel?
In how many of the distinct permutations of the letters in MISSISSIPPI do the four I’s not come together?
Find x in each of the following:
How many natural numbers not exceeding 4321 can be formed with the digits 1, 2, 3 and 4, if the digits can repeat?
How many 5-digit telephone numbers can be constructed using the digits 0 to 9. If each number starts with 67 and no digit appears more than once?
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?
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?
Evaluate each of the following:
6P6
Evaluate each of the following:
P(6, 4)
Write the number of ways in which 7 men and 7 women can sit on a round table such that no two women sit together ?
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 ?
The number of six letter words that can be formed using the letters of the word "ASSIST" in which S's alternate with other letters is
Evaluate `("n"!)/("r"!("n" - "r")!)` when n = 5 and r = 2.
Find the number of arrangements that can be made out of the letters of the word “ASSASSINATION”.
Find the rank of the word ‘CHAT’ in the dictionary.
Evaluate the following.
`(3! + 1!)/(2^2!)`
The greatest positive integer which divide n(n + 1) (n + 2) (n + 3) for all n ∈ N is:
For all n > 0, nC1 + nC2 + nC3 + …… + nCn is equal to:
Three men have 4 coats, 5 waist coats and 6 caps. In how many ways can they wear them?
Determine the number of permutations of the letters of the word SIMPLE if all are taken at a time?
Find the distinct permutations of the letters of the word MISSISSIPPI?
How many strings are there using the letters of the word INTERMEDIATE, if the vowels and consonants are alternative
How many strings are there using the letters of the word INTERMEDIATE, if all the vowels are together
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?
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?
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 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.
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 ______.
Five boys and five girls form a line. Find the number of ways of making the seating arrangement under the following condition:
| C1 | C2 |
| (a) Boys and girls alternate: | (i) 5! × 6! |
| (b) No two girls sit together : | (ii) 10! – 5! 6! |
| (c) All the girls sit together | (iii) (5!)2 + (5!)2 |
| (d) All the girls are never together : | (iv) 2! 5! 5! |
If 1P1 + 2. 2p2 + 3. 3p3 + ....... 15. 15P15 = qPr – s, 0 ≤ s ≤ 1, then q+sCr–s is equal to ______.
Ten different letters of an alphabet are given. Words with five letters are formed from these given letters. Determine the number of words which have at least one letter repeated.
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 ______.
