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Catherine rolls a standard $6$-sided die six times.  If the product of her rolls is $300,$ then how many different sequences of rolls could there have been?  (The order of the rolls matters.)

 Mar 28, 2024
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300 =   10^2 * 3  =  2 * 2 * 5 * 5 * 3 * 1

 

No. of  different sequences  =  6!  / [ (no. of 2s )! * (no. of 5s )! ] =  6! / [ 2! * 2! ] =  720 / 4  =  180

 

cool cool cool

 Mar 28, 2024

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