A die is rolled three times. Find the probabi | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) When a die is rolled three times,the total number of outcomes is $6^3 = 216$.Let the outcomes be $x_1, x_2, x_3$ such that $1 \le x_1 < x_2 < x_3

Vedclass · Accepted Answer

$\frac{20}{216}$

Vedclass · Answer

(B) When a die is rolled three times,the total number of outcomes is $6^3 = 216$.Let the outcomes be $x_1, x_2, x_3$ such that $1 \le x_1 To satisfy the condition that each number is larger than the previous one,we need to select $3$ distinct numbers from the set $\{1, 2, 3, 4, 5, 6\}$.The number of ways to choose $3$ distinct numbers is given by the combination formula $^6C_3$.$^6C_3 = \frac{6 	imes 5 	imes 4}{3 	imes 2 	imes 1} = 20$.Once $3$ distinct numbers are chosen,there is only $1$ way to arrange them in strictly increasing order.Therefore,the number of favorable outcomes is $20$.The probability is $\frac{20}{216}$.

$A$ die is rolled three times. Find the probability of getting a larger number than the previous number each time.

Similar Questions

The number of ways of distributing $8$ identical rings to $3$ different girls so that every girl gets at least $1$ ring is

In how many ways can $10$ balls be divided between two boys,such that one receives $2$ balls and the other receives $8$ balls?

There are $4$ oranges,$5$ apples,and $7$ mangoes in a fruit basket. The number of ways of selecting at least one fruit from among the fruits in the basket is

$A$ village has $10$ players. $A$ team of $6$ players is to be formed. $5$ members are chosen out of these $10$ players and then the captain is chosen from the remaining $5$ players. The total number of ways of choosing such a team is:

$^nC_r + ^nC_{r-1}$ is equal to

Vedclass Test Series

Exam Paper Generator

Online Exam Module