A) \[^{9}{{C}_{3}}\]
B) \[^{10}{{C}_{3}}\]
C) \[^{9}{{P}_{3}}\]
D) \[^{10}{{P}_{3}}\]
Correct Answer: A
Solution :
[a]\[{{x}_{1}}<{{x}_{2}}<{{x}_{3}}<{{x}_{4}}<{{x}_{5}}<{{x}_{6}},\]when the number Is \[{{x}_{1}}{{x}_{2}}{{x}_{3}}{{x}_{4}}{{x}_{5}}{{x}_{6}}\]clearly no digit can be zero. Also, all the digits are distinct. So. Let us first select six digits from the list of digits 1, 2, 3, 4, 5, 6, 7, 8, 9, which can be done in \[^{9}{{C}_{6}}\] ways. After selecting these digits they can be put only in one order. Thus, total number of such numbers is \[^{9}{{C}_{6}}\times 1{{=}^{9}}{{C}_{3.}}\]
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