+0  
 
0
8
1
avatar+624 

Catherine rolls a standard 6-sided die eight times. If the product of her rolls is 2700, then how many different sequences of rolls could there have been? (The order of the rolls matters.)

 Mar 3, 2024
 #1
avatar+128794 
+1

prime factorization of  2700  =  2^2 * 3^3 * 5^2

 

Possible Factorizations       Number  of  identifiable sequences

22333551                             8! / (2! * 3! * 2!)  = 3360

43335511                             8! /( 2! * 3! * 2! ) = 3360

62335511                             8! / ( 2! * 2! * 2!) =  5040

66355111                             8! / ( 2! * 2! * 3!) =  3360

 

Total possible sequences  =   3 (3360) + 5040  =  15120

 

cool cool cool

 Mar 3, 2024
edited by CPhill  Mar 3, 2024

1 Online Users

avatar