MOTORCYCLE Parking

Probability Level 1

If there are $abcdef$ distinct arrangements for the letters of the word MOTORCYCLE, find $a+b+c+d+e+f$ .

Details and Assumptions

$abcdef$ is a 6-digit number.

An arrangement does not have to be readable, one arrangement can be " RMTOOCCLYE ".

Note : This question is taken from the Mathizen Question of the Day.

1 solution

Hillary Diane Andales
May 19, 2014

There are 10! arrangements for MOTORCYCLE. But not all are distinct, there are 2 O's and 2 C's. To compensate for these repetitions, solve:

$\frac{10!}{2! \times 2!} = \frac{10 \times 9 \times 8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1}{2 \times 1 \times 2 \times 1}$

Solving gives $abcdef = 907200$ . So, $a + b + c + d + e + f = \boxed{18}$

Yeah i got that 18. But what does it shouldnt be readable mean?

chetan shah - 6 years, 11 months ago