10 In how many ways can one to put seven different colored balls into six identical boxes, if some boxes can remain empty? 121; 2470; 3 140; 4301; 5 235; 6 63; 7876; 8 350.
10 In how many ways can one to put seven different colored balls into six identical boxes, if some boxes can remain empty? 121; 2470; 3 140; 4301; 5 235; 6 63; 7876; 8 350.
Chapter9: Sequences, Probability And Counting Theory
Section9.5: Counting Principles
Problem 40SE: A family consisting of 2 parents and 3 children is to pose for a picture with 2 family members in...
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Transcribed Image Text:10
In how many ways can one to put seven different colored balls into six identical boxes,
if some boxes can remain empty ?
121; 2470; 3 140;
301;
5 235; 6 63;
876;
8 350.
A password consists of six symbols
First symbol is an element of set {F, B, P, K, R, G, D, L, S}.
Second and third elements are from set {d, g, s, r, m, q, e, f, v,c}.
Last three symbols are digits 0,1, ..., 8, 9.
How many different password can be made, if all three symbols must be different?
(Combinations 021 or 120 are allowed, but combinations 100 or 011 - no.)
(1) 648899; 2 648000; (3) 648338; (4) 647685; 5 648261; (6 810000.
12
Which collection of sets is set's {u, p, v, d, e, q, z, f, t} partition?
A = {{e, f, p. q},
{t, z, u}, {v,d}}; B = {{e, f,t, z}, {u, v,g}, {d}}.
4 both.
B; 2 no one; 3 A;
13
How many such partitions exists?
10022; (2) 118124; (3) 1624; 4 3025; (5) 2941; (6) 9330.
14
Which set of cycles is equal to
set of cycles {(w, p, v), (u, s, r),
A= {(c, a), (s, r, u), (p, w, v)};
1 B; 2 A; 3 no one; 4 both.
set's {v, u, p, a, c, w, s, r}
(c, a)}?
B = {(a, c), (v, w, p), (u,s,r)}.
15
How many such sets of cycles exists?
(1) 1172700; (2) 301; (3) 13132; 4 966; (5) 76855; (6) 11186.
11
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