If 8 cdot {}^{7}P_{r} = 7 cdot {}^{8}P_{r-1}, | vedclass

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

Question

(D) Given equation: $8 \cdot {}^{7}P_{r} = 7 \cdot {}^{8}P_{r-1}$ Using the formula ${}^{n}P_{r} = \frac{n!}{(n-r)!}$: $8 \cdot \frac{7!}{(7-r)!} = 7

Vedclass · Accepted Answer

No solution (No such $r$ exists)

Vedclass · Answer

(D) Given equation: $8 \cdot {}^{7}P_{r} = 7 \cdot {}^{8}P_{r-1}$ Using the formula ${}^{n}P_{r} = \frac{n!}{(n-r)!}$: $8 \cdot \frac{7!}{(7-r)!} = 7 \cdot \frac{8!}{(8-(r-1))!} $ $8 \cdot \frac{7!}{(7-r)!} = 7 \cdot \frac{8!}{(9-r)!} $ Since $8! = 8 \cdot 7!$,we have: $\frac{8 \cdot 7!}{(7-r)!} = \frac{7 \cdot 8 \cdot 7!}{(9-r)!} $ $\frac{1}{(7-r)!} = \frac{7}{(9-r)(8-r)(7-r)!} $ $1 = \frac{7}{(9-r)(8-r)} $ $(9-r)(8-r) = 7 $ $72 - 9r - 8r + r^2 = 7 $ $r^2 - 17r + 65 = 0 $ Using the quadratic formula $r = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$: $r = \frac{17 \pm \sqrt{289 - 260}}{2} = \frac{17 \pm \sqrt{29}}{2} $ Since $r$ must be a non-negative integer,there is no such $r$ that satisfies the equation. Thus,the correct option is $D$.

If $8 \cdot {}^{7}P_{r} = 7 \cdot {}^{8}P_{r-1}$,what is the value of $r$?

Similar Questions

There are $15$ stations on a train route and the train has to be stopped at exactly $5$ stations among these $15$ stations. If it stops at at least two consecutive stations,then the number of ways in which the train can be stopped is

The number of $4$-digit numbers that are not divisible by $5$ is:

$A$ $5$-digit number $\overline{abcde}$,when multiplied by $9$,gives the $5$-digit number $\overline{edcba}$. The sum of the digits in the number is:

All the letters of the word $TABLE$ are permuted and the strings of letters (may or may not have meaning) thus formed are arranged in dictionary order. Then the rank of the word $TABLE$ counted from the rank of the word $BLATE$ is

If the letters of the word $ATTEMPT$ are rearranged randomly,what is the probability that all $T$'s occur together?

Vedclass Test Series

Exam Paper Generator

Online Exam Module