A) \[\frac{1}{5\,!}\]
B) \[\frac{50\,!}{55\,!}\]
C) \[\frac{1}{{{50}^{5}}}\]
D) None of these
Correct Answer: A
Solution :
Five places for 5 volumes of Mathematics from 25 places of books can be select in \[{}^{25}{{C}_{5}}\] ways. In these places, we are not to permute the 5 volumes since order of these 5 volumes is fixed i.e., \[{{v}_{1}},\,{{v}_{2}},\,{{v}_{3}},\,{{v}_{4}},\,{{v}_{5}}.\] Remaining 20 books can be arranged in \[20\,\,!\] ways. \[\therefore \] Favourable ways \[={}^{25}{{C}_{5}}.\,20\,\,!=\frac{25\,\,!\,.\,20\,\,!}{5\,\,!\,\,20\,\,!}=\frac{25\,\,!}{5\,\,!}\] Also total number of ways \[=25\,\,!\] \[\therefore \] Probability \[=\frac{25\,\,!}{5\,\,!\,\,25\,\,!}=\frac{1}{5\,\,!}\].
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