Advertisements
Advertisements
प्रश्न
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?
उत्तर
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
संबंधित प्रश्न
Is 3! + 4! = 7!?
How many 3-digit numbers can be formed by using the digits 1 to 9 if no digit is repeated?
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 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 ?
If three six faced die each marked with numbers 1 to 6 on six faces, are thrown find the total number of possible outcomes ?
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?
Three dice are rolled. Find the number of possible outcomes in which at least one die shows 5 ?
In how many ways can 5 different balls be distributed among three boxes?
Evaluate each of the following:
8P3
Evaluate each of the following:
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.
Write the remainder obtained when 1! + 2! + 3! + ... + 200! is divided by 14 ?
The number of words from the letters of the word 'BHARAT' in which B and H will never come together, is
If in a group of n distinct objects, the number of arrangements of 4 objects is 12 times the number of arrangements of 2 objects, then the number of objects 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 different ways in which 8 persons can stand in a row so that between two particular persons A and B there are always two persons, is
How many six-digit telephone numbers can be formed if the first two digits are 45 and no digit can appear more than once?
In how many ways 5 boys and 3 girls can be seated in a row, so that no two girls are together?
Find the number of arrangements that can be made out of the letters of the word “ASSASSINATION”.
Evaluate the following.
`((3!)! xx 2!)/(5!)`
The possible outcomes when a coin is tossed five times:
The number of ways to arrange the letters of the word “CHEESE”:
Determine the number of permutations of the letters of the word SIMPLE if all are taken at a time?
A test consists of 10 multiple choice questions. In how many ways can the test be answered if each question has four choices?
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 strings are there using the letters of the word INTERMEDIATE, if no two 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 divisible by 4?
Find the sum of all 4-digit numbers that can be formed using digits 1, 2, 3, 4, and 5 repetitions not allowed?
Find the sum of all 4-digit numbers that can be formed using digits 0, 2, 5, 7, 8 without repetition?
In how many ways can 5 children be arranged in a line such that two particular children of them are never together.
The number of 5-digit telephone numbers having atleast one of their digits repeated is ______.
The number of permutations of n different objects, taken r at a line, when repetitions are allowed, 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! |
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 |
