hi tys question but im facing abit of difficulty
qn: group of diplomats chosen to represent 3 islands, K,L and M
. group is to consist of 8 diplomats and is chosen from a set of 12
diplomats consisting of 3 from k, 4 from L and 5 from M . Find the
number of ways the group can be chosen if it includes
a) diplomats from L and M only
i did it like this:
case 1: 4 from M, 4 from L = 5c4 X 4c4 = 5
case 2: 5 from M , 3 from L = 5c1 X 4c3 = 20
therefore total ways is 25 .
but ans is 9 ( from tys)
b)at least 4 diplomats from M
i did it like this
C1: 4M, 4 L =5
C2: 4M, 3L, 1K = 5c4 . 4c3 . 3c1 =5.4.3=60
C3: 4M, 3K, 1L = 5c4 . 3c3 . 4c1=5.1.4=20
C4: 4M,2L,2K = 5c4 . 4c2. 3c2 =5.6.3=90
C5:4M,2K,2L=90
C6:5M,3L = 5c5. 4c3= 1.4=4
C7: 5M,3K = 5c5 . 3c3 =1
C8: 5M,1K,2L = 5c5 . 3c1 . 4c2 =1.3.6=18
C9: 5M,2K,1L = 5c5 . 3c2 . 4c1= 1.3.4=12
total is 290 .
ans from tys is 210
am i wrong or is the tys wrong? if so , where have i gone wrong?
teach me thanks xD