Question

find the total number of ways to distribute four prices among 5 students if no Student gets all prizes.​

Answer 1

$\huge{\underline{\sf{\red{Answer}}}}$

Given:

Number of prizes = 4

Each price has 5 options

______________________________________

★ Important ★

❝ No student Receives all the prizes ❞

______________________________________

$\huge{\underline{\tt{SoluTion}}}$

Number of ways will be 5⁴

and case when one student Receives all prizes gets subtracted

$\therefore \implies 5^4 -5 \\ \implies 625 -5 \\ \boxed{620}$

Answer 2

$\huge{\underline{\underline{\mathfrak{Question}}}}$

Find the total number of ways to distribute four prices among 5 students if no Student gets all prizes.

$\huge{\underline{\underline{\mathfrak{Given}}}}$

Number of prizes = 4

Each price has 5 options

$\huge{\underline{\underline{\mathfrak{Answer}}}}$

$no.of \: ways = {5}^{4}$

And case when one student received all prizes gets subtracted.

$= > {5}^{4} - 5$

$= > 625 - 5$

$= > 620$

______________________________________

$\huge{\underline{\underline{\mathfrak{Thank you}}}}$