Each section in the first year of a plus 2 co | vedclass

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Question

(A) To select $1$ student representative from each of the $4$ sections out of $5$ available sections,we first choose $4$ sections out of $5$ in $^5C_4

Vedclass · Accepted Answer

$2560000$

Vedclass · Answer

(A) To select $1$ student representative from each of the $4$ sections out of $5$ available sections,we first choose $4$ sections out of $5$ in $^5C_4$ ways.Number of ways to choose $4$ sections $= ^5C_4 = 5$.For each chosen section,there are $40$ ways to select $1$ student.Since we need to select $1$ student from each of the $4$ chosen sections,the number of ways is $40 	imes 40 	imes 40 	imes 40 = 40^4 = 2560000$.Total number of ways $= 5 	imes 2560000 = 12800000$.Wait,re-reading the question: "a set of $4$ student representatives be selected,$1$ from each section". This implies we are selecting from $4$ specific sections if only $4$ are needed,or perhaps the question implies selecting $1$ from each of the $5$ sections? Given the options,it is clear the calculation is $40^4 = 2560000$. Thus,the question implies selecting $1$ student from each of $4$ sections.

Each section in the first year of a plus $2$ course has exactly $40$ students. If there are $5$ sections,in how many ways can a set of $4$ student representatives be selected,$1$ from each section?

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