Non-repeating 30101

1. How many different options are there for exchanging a ten-euro bill with one-euro, two-euro, and five-euro bills?
a) 5 b) 8 c) 14 d) 10

2. How many non-repeating three-digit numbers can be written using odd digits?
a) 999 b) 225 c) 60 d) 25

Correct answer:

n₁ =  10
n₂ =  60

Step-by-step explanation:

$$\begin{gathered} 10=1a+2b+5c \\ {a}_1=0,b_1=0,c_1=2 \\ {a}_2=0,b_2=5,c_2=0 \\ {a}_3=1,b_3=2,c_3=1 \\ {a}_4=2,b_4=4,c_4=0 \\ {a}_5=3,b_5=1,c_5=1 \\ {a}_6=4,b_6=3,c_6=0 \\ {a}_7=5,b_7=0,c_7=1 \\ {a}_8=6,b_8=2,c_8=0 \\ {a}_9=8,b_9=1,c_9=0 \\ {a}_{10}=10,b_{10}=0,c_{10}=0 \\ {n}_1=10 \end{gathered}$$

$$\begin{gathered} 1,3,5,7,9 \\ {n}_2=5\cdot 4\cdot 3=60 \end{gathered}$$

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