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MathNet 2019-part-02 — 184 problems (EN–VI) Question 21

Math Olympiad Vault · MathNet 2019-part-02 — 184 problems (EN–VI)

Question 21

Five friends are the starters of a volleyball team. Their shirts are numbered on the back with the first 5 positive odd numbers. Ana is number 1; Bia is number 3; Cátia is number 5; Dani is number 7; and Esmeralda is number 9. During practice the five friends line up to form numbers with their shirts, all with 5 digits. For example, the line with Esmeralda, Dani, Cátia, Bia and Ana, in this order, forms the number 97531.

a) How many different numbers can they form?
b) How many numbers can be formed if Cátia cannot be first in line?
c) How many numbers can be formed if Esmeralda and Bia stand side by side?
d) Fábia, shirt number 11, decides to join the game. How many numbers are formed now?