Discussion
Five digit number is formed using the digits 0,1,2,3,4 and 5 without repetitions. Number of five digit numbers which are divisible by 10 is
Answer: C
There are 120 such numbers.
A number divisible by 10 must end in 0. With 0 fixed in the units place, the other four places are filled from the remaining five digits 1, 2, 3, 4, 5 without repetition, and the leading digit can no longer be 0:
\[ {}^{5}P_{4} = 5 \times 4 \times 3 \times 2 = 120 \]
240 and 360 count numbers ending in 0 or 5 (divisible by 5) or ignore the restriction, and the larger values count five-digit numbers in general.
Remember that 75% and 87.5% completion take two and three half-lives respectively, which is the quickest way to test such statements.
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