A) \[^{4}{{P}_{4}}\]
B) \[^{4}{{P}_{3}}\]
C) \[^{4}{{P}_{1}}{{+}^{4}}{{P}_{2}}{{+}^{4}}{{P}_{3}}\]
D) \[^{4}{{P}_{1}}{{+}^{4}}{{P}_{2}}{{+}^{4}}{{P}_{3}}{{+}^{4}}{{P}_{4}}\]
Correct Answer: D
Solution :
Number of 1 digit numbers \[{{=}^{4}}{{P}_{1}}\] Number of 2 digit numbers \[{{=}^{4}}{{P}_{2}}\] Number of 3 digit numbers \[{{=}^{4}}{{P}_{3}}\] Number of 4 digit numbers \[{{=}^{4}}{{P}_{4}}\] Hence the required number of ways \[{{=}^{4}}{{P}_{1}}{{+}^{4}}{{P}_{2}}{{+}^{4}}{{P}_{3}}{{+}^{4}}{{P}_{4}}\].
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