If four-digit numbers are formed by using the | vedclass

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

Question

(B) number is divisible by $25$ if its last two digits are $25, 50,$ or $75$. Given the set of digits $\{1, 2, 3, 4, 5, 6, 7\}$,the possible two-digit

Vedclass · Accepted Answer

$40$

Vedclass · Answer

(B) number is divisible by $25$ if its last two digits are $25, 50,$ or $75$. Given the set of digits $\{1, 2, 3, 4, 5, 6, 7\}$,the possible two-digit endings divisible by $25$ are $25$ and $75$ (since $50$ is not possible as $0$ is not in the set). Case $1$: The number ends in $25$. The last two digits are fixed as $2$ and $5$. The remaining $2$ positions can be filled by the remaining $5$ digits $\{1, 3, 4, 6, 7\}$ in $P(5, 2) = 5 	imes 4 = 20$ ways. Case $2$: The number ends in $75$. The last two digits are fixed as $7$ and $5$. The remaining $2$ positions can be filled by the remaining $5$ digits $\{1, 2, 3, 4, 6\}$ in $P(5, 2) = 5 	imes 4 = 20$ ways. Total numbers divisible by $25 = 20 + 20 = 40$.

If four-digit numbers are formed by using the digits $1, 2, 3, 4, 5, 6, 7$ without repetition,then how many of these numbers are exactly divisible by $25$?

Similar Questions

The number of words that can be formed by using the letters of the word $CALCULATE$ such that each word starts and ends with a consonant,are

How many even numbers of $3$ different digits can be formed from the digits $1, 2, 3, 4, 5, 6, 7, 8, 9$ (repetition is not allowed)?

Find $r$ if $^{5}P_{r} = ^{6}P_{r-1}$.

The number of ways in which the following prizes can be given to a class of $20$ boys,first and second Mathematics,first and second Physics,first Chemistry,and first English is:

Eight different letters of an alphabet are given. Words of four letters from these are formed. The number of such words with at least one letter repeated is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module