Question

Please help with D and E, also if you can take a look at abc and let me know if I’m on the right track with those I’d really appreciate it

Lp 721 Win Question 3. Let S (1,2,... , 100). How many (a) 10-combinations are there of S? 100 P(IU, ro Cembo! Io0! r(n-r)| ID I (b) 10-combinations are there of S such that 2 does not appear? (100-1q) S=91 (c) 10-combinations are there of S such that 2 does appear? 00190 10-combinations are there of S that contain exactly four even numbers? lotal - o !does tur (d) (e) combinations of S have no more than four elements total?

Answer 1

d) 10 -combinations of S that contain 4 even numbers =N(selecting 4 even numbers from 50 even numbers and 6 odd numbers from 50 odd numbers) =C(50,4)*C(50,6)=(50!/(4!*46!))*(50!/(6!*44!))

=230300*15890700 =3659628210000

e)

number of combinations =N(0 elements)+N(1 element)+N(2 element)+N(3 element)+N(4 element)

=C(100,0)+C(100,1)+C(100,2)+C(100,3)+C(100,4)=1+100+4950+161700+3921225 =4087976