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If (A) has (5) elements and (B) has (3) elements, how many functions from (A) to (B) have range exactly of size (2)?यदि (A) में (5) अवयव और (B) में (3) अवयव हैं, तो (A) से (B) में ऐसे फलनों की संख्या कितनी है जिनका परास ठीक (2) अवयवों का हो?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: (90)(90)
Step 1: Choose the (2) elements of the range in (\binom{3}{2}=3) ways. Step 2: Onto functions onto these two chosen elements are (2^5-2=30). Step 3: Total number is (3\cdot30=90).चरण 1: परास के (2) अवयव चुनने के तरीके (\binom{3}{2}=3) हैं। चरण 2: चुने हुए दो अवयवों पर आच्छादी फलन (2^5-2=30) होंगे। चरण 3: कुल संख्या (3\cdot30=90) होगी।
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