Chapter 6 - Section 6.3 - Permutations and Combinations - Exercises - Page 414: 38

62,994,022,035,644,700 ways to select 12 countries as a council

Ways to select 3 from 45 = $C$(45,3) = 14190 Ways to select 4 from 57 = $C$(57,4) = 395010 Remaining countries = 12 - (3 + 4) = 5 Ways to select 5 from 69 = $C$(69,5) = 11238513 Using product rule , Ways to select 12 countries = 14190$\times$395010$\times$11238513 = 62,994,022,035,644,700