Five-digit numbers are formed using the digit | vedclass

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

Question

(A) The set of available digits is ${1, 2, 3, 4, 5, 6, 8}$. There are $7$ digits in total.Total number of $5$-digit numbers that can be formed using t

Vedclass · Accepted Answer

$\frac{2}{7}$

Vedclass · Answer

(A) The set of available digits is ${1, 2, 3, 4, 5, 6, 8}$. There are $7$ digits in total.Total number of $5$-digit numbers that can be formed using these $7$ digits (assuming repetition is not allowed) is $^7P_5 = 7 	imes 6 	imes 5 	imes 4 	imes 3 = 2520$.Even digits available in the set are ${2, 4, 6, 8}$,which are $4$ in total.For a $5$-digit number to have even digits at both ends,we must choose $2$ even digits for the two ends from the $4$ available even digits. The number of ways to arrange these is $^4P_2 = 4 	imes 3 = 12$.After placing $2$ even digits at the ends,we are left with $5$ digits (from the original $7$ digits minus the $2$ used). We need to fill the remaining $3$ positions using these $5$ digits. The number of ways to do this is $^5P_3 = 5 	imes 4 	imes 3 = 60$.Total favorable outcomes = $12 	imes 60 = 720$.Probability = $\frac{	ext{Favorable outcomes}}{	ext{Total outcomes}} = \frac{720}{2520} = \frac{72}{252} = \frac{2}{7}$.

Five-digit numbers are formed using the digits $1, 2, 3, 4, 5, 6$,and $8$. What is the probability that they have even digits at both the ends?

Similar Questions

$A$ bag $x$ contains $3$ white balls and $2$ black balls and another bag $y$ contains $2$ white balls and $4$ black balls. $A$ bag and a ball out of it are picked at random. The probability that the ball is white,is

In a single throw of $2$ dice,find the probability of getting a total of $11$.

$2$ dice are thrown. Find the probability of getting a multiple of $3$ as the sum.

An $URN$ contains $6$ blue,$4$ red,$3$ green and $2$ yellow marbles. If four marbles are picked at random,what is the probability that one is yellow,two are red and one is blue?

$A$ coin is tossed until a head appears or until the coin has been tossed five times. If a head does not occur on the first two tosses,then the probability that the coin will be tossed $5$ times is

Vedclass Test Series

Exam Paper Generator

Online Exam Module