(a) In how many ways can a class of 12 students be divided into groups of 3? (b)
ID: 3257403 • Letter: #
Question
(a) In how many ways can a class of 12 students be divided into groups of 3? (b) In how many ways can a judge award first, second, and third prize in a competition of 18 participants? (c) In how many ways can 10 toys be divided among 5 children if each is to receive 2 toys? (d) In how many ways can 9 toys be distributed among 4 children if the youngest child must receive 3 toys and each of other children is to receive 2 toys? (e) From a deck of 52 cards, how many 5 cards can be formed that contain (i) exactly 3 aces? (ii) At least 3 hearts? (iii) at most 2 faces?Explanation / Answer
4a) 12c3=220
b)18c3*3!=816*6=4896
c)10c2*8C2*6C2*4c2*2c2=45*28*15*6*1=113400
e)52c5(p)^3*(q)2 here p=4/52 q=1-p
ii)p(3)+p(4)+p(5) here p=13/52
iii)P(0)+(1) here p=12/52
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