Advertisements
Advertisements
प्रश्न
Three dice are rolled. Find the number of possible outcomes in which at least one die shows 5 ?
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
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?
Find r if `""^5P_r = 2^6 P_(r-1)`
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!
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?
Find the number of ways in which 8 distinct toys can be distributed among 5 childrens.
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 words that can be formed out of the letters of the word 'COMMITTEE' ?
Write the number of ways in which 6 men and 5 women can dine at a round table if no two women sit together ?
Write the number of numbers that can be formed using all for digits 1, 2, 3, 4 ?
The number of five-digit telephone numbers having at least one of their digits repeated is
The number of different signals which can be given from 6 flags of different colours taking one or more at a time, is
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
In a room there are 12 bulbs of the same wattage, each having a separate switch. The number of ways to light the room with different amounts of illumination is
Find x if `1/(6!) + 1/(7!) = x/(8!)`
If (n+2)! = 60[(n–1)!], find n
Evaluate the following.
`(3! + 1!)/(2^2!)`
If n is a positive integer, then the number of terms in the expansion of (x + a)n is:
A test consists of 10 multiple choice questions. In how many ways can the test be answered if the first four questions have three choices and the remaining have five choices?
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.
What is the maximum number of different answers can the students give?
8 women and 6 men are standing in a line. How many arrangements are possible if any individual can stand in any position?
In how many ways 4 mathematics books, 3 physics books, 2 chemistry books and 1 biology book can be arranged on a shelf so that all books of the same subjects are together
A coin is tossed 8 times, how many different sequences containing six heads and two tails are possible?
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 of these 6-digit numbers are even?
Find the number of strings that can be made using all letters of the word THING. If these words are written as in a dictionary, what will be the 85th string?
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.
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 ______.
The number of 5-digit telephone numbers having atleast one of their digits repeated is ______.
The number of different words that can be formed from the letters of the word INTERMEDIATE such that two vowels never come together is ______.
The number of three-digit even numbers, formed by the digits 0, 1, 3, 4, 6, 7 if the repetition of digits is not allowed, is ______.
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 ______.
