Advertisements
Advertisements
Question
Write the total number of possible outcomes in a throw of 3 dice in which at least one of the dice shows an even number.
Advertisements
Solution
Total number of outcomes when 3 dice are thrown = `6xx6xx6=216`
Number of outcomes in which there is an odd number on all the three dice =`3xx3xx3=27`
∴ Number of outcomes in which there is an even number at least on one dice = {Total possible outcomes}- {Number of outcomes in which there is an odd number on all the three dice } =`216xx27=189`
APPEARS IN
RELATED QUESTIONS
Evaluate 4! – 3!
Evaluate `(n!)/((n-r)!)`, when n = 9, r = 5
How many 4-digit numbers are there with no digit repeated?
How many 3-digit even numbers can be made using the digits 1, 2, 3, 4, 6, 7, if no digit is repeated?
In how many ways can the letters of the word PERMUTATIONS be arranged if the words start with P and end with S.
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.
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 ?
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 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?
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 ?
Evaluate each of the following:
8P3
Evaluate each of the following:
P(6, 4)
In how many ways can 4 letters be posted in 5 letter boxes?
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 ?
How many numbers greater than 10 lacs be formed from 2, 3, 0, 3, 4, 2, 3 ?
The number of ways in which the letters of the word 'CONSTANT' can be arranged without changing the relative positions of the vowels and 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
Evaluate `("n"!)/("r"!("n" - "r")!)` when n = 5 and r = 2.
Evaluate the following.
`(3! + 1!)/(2^2!)`
For all n > 0, nC1 + nC2 + nC3 + …… + nCn is equal to:
The total number of 9 digit number which has all different digit is:
The number of ways to arrange the letters of the word “CHEESE”:
The number of words with or without meaning that can be formed using letters of the word “EQUATION”, with no repetition of letters is:
8 women and 6 men are standing in a line. How many arrangements are possible if any individual can stand in any position?
8 women and 6 men are standing in a line. In how many arrangements will all 6 men be standing next to one another?
How many ways can the product a2 b3 c4 be expressed without exponents?
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
Find the sum of all 4-digit numbers that can be formed using digits 0, 2, 5, 7, 8 without repetition?
Choose the correct alternative:
If Pr stands for rPr then the sum of the series 1 + P1 + 2P2 + 3P3 + · · · + nPn is
Three married couples are to be seated in a row having six seats in a cinema hall. If spouses are to be seated next to each other, in how many ways can they be seated? Find also the number of ways of their seating if all the ladies sit together.
Find the number of permutations of n different things taken r at a time such that two specific things occur 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?
The number of different words that can be formed from the letters of the word INTERMEDIATE such that two vowels never come together 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 m+nP2 = 90 and m–nP2 = 30, then (m, n) is given by ______.
