Answer:
2,042,975
Explanation:
Josh can choose 9 of his 25 classmates using the function C(n,k), which tells the number of combinations of n objects taken k at a time.
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Here, Josh wants to choose 9 from 25 classmates. The number of possible choices is ...
C(n, k) = n!/(k!(n-k)!)
C(25, 9) = 25!/(9!(25 -9)!) = 25·24·23·22·21·20·19·18·17÷(9·8·7·6·5·4·3·2·1)
= 2,042,975
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Additional comment
In effect, the first ticket can go to any of 25 classmates, the second to any of 24, and so on. The last ticket can go to any of 17 classmates. This product 25·24·...·17 counts each group of classmates 9! times. Since the order in which they are chosen does not matter, the final number is then ...
25!/(16!·9!) = 2042975