Four-digit numbers with all digits distinct a | vedclass

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

Question

(A) Total four-digit numbers formed using $7$ distinct digits is $p = P(7, 4) = 7 	imes 6 	imes 5 	imes 4 = 840$. To find $q$ (numbers $> 3400$): C

Vedclass · Accepted Answer

$3: 2$

Vedclass · Answer

(A) Total four-digit numbers formed using $7$ distinct digits is $p = P(7, 4) = 7 	imes 6 	imes 5 	imes 4 = 840$. To find $q$ (numbers $> 3400$): Case $1$: Numbers starting with $4, 5, 6, 7$. The first digit can be chosen in $4$ ways,and the remaining $3$ positions can be filled by the remaining $6$ digits in $P(6, 3) = 6 	imes 5 	imes 4 = 120$ ways. Total $= 4 	imes 120 = 480$. Case $2$: Numbers starting with $3$. The second digit must be $\geq 4$. If the second digit is $4$,the remaining $2$ positions can be filled by the remaining $5$ digits in $P(5, 2) = 5 	imes 4 = 20$ ways. If the second digit is $5, 6, 7$ ($3$ choices),the remaining $2$ positions can be filled by the remaining $5$ digits in $P(5, 2) = 20$ ways. Total $= 3 	imes 20 = 60$. Thus,$q = 480 + 20 + 60 = 560$. Therefore,$p: q = 840: 560 = 3: 2$.

Four-digit numbers with all digits distinct are formed using the digits $1, 2, 3, 4, 5, 6, 7$ in all possible ways. If $p$ is the total number of numbers thus formed and $q$ is the number of numbers greater than $3400$ among them,then $p: q=$

Similar Questions

The remainder obtained when $1! + 2! + 95!$ is divided by $15$ is

If the letters of the word $INTERMEDIATE$ are arranged,what is the probability that the two $E$'s do not come together?

If ${ }^{n} P_{r}={ }^{n} P_{r+1}$ and ${ }^{n} C_{r}={ }^{n} C_{r-1}$,then the value of $r$ is equal to:

If $_n{P_4} = 24 \times \binom{n}{5}$,then $n = \dots$

In a relay race there are five teams $A, B, C, D$ and $E$. What is the probability that $A, B$ and $C$ are the first three to finish (in any order)? (Assume that all finishing orders are equally likely.)

Vedclass Test Series

Exam Paper Generator

Online Exam Module