Question

Of 8 household chores in how many ways can you do three fourths of them?

Answer 1

Three fourths of 8=3×8/4=6.

The number of ways of doing 6 out of 8 different chores is 28 (combinations).

If the chores are labelled A, B, C, D, E, F, G, H then we have the following combinations:
CDEFGH BDEFGH BCEFGH BCDFGH BCDEGH BCDEFH BCDEFG (7)
ADEFGH ACEFGH ACDFGH ACDEGH ACDEFH ACDEFG (6)

ABEFGH ABDFGH ABDEGH ABDEFH ABDEFG (5)

ABCFGH ABCEGH ABCEFH ABCEFG (4)
ABCDGH ABCDFH ABCDFG (3)
ABCDEH ABCDEG (2)

ABCDEF (1)

7+6+5+4+3+2+1=28.

If the order of the chores counts then we need to multiply 28 by 720 (the number of ways 6 different chores can be arranged in order). This comes to 20160.