| If a 4 digit number is formed at random using the digits 1, 3, 5, 7 and 9 without repetition, thus the probability that it is divisible by 5 is |
A) \[\frac{4}{5}\]
B) \[\frac{3}{2}\]
C) \[\frac{1}{5}\]
D) \[\frac{2}{3}\]
Correct Answer: C
Solution :
| Number of four-digit numbers which are formed with |
| \[1,\]\[3,\]\[5,\]\[7,\]\[9={}^{5}{{P}_{4}}\] |
| \[=5\times 4\times 3\times 2=120=n\,\,(s)\] |
| The number which are divisible by \[5={}^{4}{{P}_{3}}\] |
| \[=4\times 3\times 2=24=n\,\,(E)\] |
| \[\therefore \] \[P\,\,(E)=\frac{n\,\,(E)}{n\,\,(S)}=\frac{24}{120}=\frac{1}{5}\] |
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