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What is the value of \(\frac{5!}{1!,4!}\)?\(\frac{5!}{1!,4!}\) का मान क्या है?
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Correct answer:सही उत्तर: 55
Since \(5!=5\times4!\) and \(1!=1\), \(\frac{5!}{1!,4!}=\frac{5\times4!}{1\times4!}=5\). The value 10 is \(\binom{5}{2}\), but the denominator here is \(1!\,4!\); hence the expression equals \(\binom{5}{1}=5\). Exam tip: In factorial fractions, cancel common factorial terms first.क्योंकि \(5!=5\times4!\) और \(1!=1\), इसलिए \(\frac{5!}{1!,4!}=\frac{5\times4!}{1\times4!}=5\)। विकल्प 10, \(\binom{5}{2}\) का मान है, लेकिन यहाँ हर में \(1!\,4!\) है; अतः यह \(\binom{5}{1}=5\) के बराबर है। परीक्षा टिप: फैक्टोरियल भिन्नों में समान फैक्टोरियल पदों को पहले काटें।
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