Advertisements
Advertisements
Question
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?
Advertisements
Solution
Total number of outcomes when a coin is tossed once = 2 (Heads, Tails)
Number of outcomes when the coin is tossed for the second time = 2
∴ Number of outcomes when the coin is tossed thrice = `2xx2xx2=8`
Similarly, the number of outcomes when the coin is tossed four times =`2xx2xx2xx2=16`
Similarly, the number of outcomes when the coin is tossed five times =`2xx2xx2xx2xx2=32`
Similarly, the number of outcomes when the coin is tossed 'n' times = `2xx2xx.......n`times `= 2^n`
APPEARS IN
RELATED QUESTIONS
Is 3! + 4! = 7!?
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?
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 one can post 5 letters in 7 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:
Write the number of arrangements of the letters of the word BANANA in which two N's come together.
Write the number of ways in which 5 boys and 3 girls can be seated in a row so that each girl is between 2 boys ?
Write the remainder obtained when 1! + 2! + 3! + ... + 200! is divided by 14 ?
Number of all four digit numbers having different digits formed of the digits 1, 2, 3, 4 and 5 and divisible by 4 is
A 5-digit number divisible by 3 is to be formed using the digits 0, 1, 2, 3, 4 and 5 without repetition. The total number of ways in which this can be done is
The number of words that can be made by re-arranging the letters of the word APURBA so that vowels and consonants are alternate is
If (n+2)! = 60[(n–1)!], find n
If `""^(("n" – 1))"P"_3 : ""^"n""P"_4` = 1 : 10 find n
Three men have 4 coats, 5 waist coats and 6 caps. In how many ways can they wear them?
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?
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?
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?
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
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 divisible by 4?
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?
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)`
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 ______.
How many words (with or without dictionary meaning) can be made from the letters of the word MONDAY, assuming that no letter is repeated, if
| C1 | C2 |
| (a) 4 letters are used at a time | (i) 720 |
| (b) All letters are used at a time | (ii) 240 |
| (c) All letters are used but the first is a vowel | (iii) 360 |
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 ______.
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.
If m+nP2 = 90 and m–nP2 = 30, then (m, n) is given by ______.
The number of permutations by taking all letters and keeping the vowels of the word ‘COMBINE’ in the odd places is ______.
