What is the digit in the ten's place of 23^(41)*25^(40)? How do you calculate this? The usual method for this kind of problem is using the Binomial theorem.

benatudq 2022-10-23 Answered
What is the digit in the ten's place of 23 41 25 40 ? How do you calculate this? The usual method for this kind of problem is using the Binomial theorem.
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Answers (2)

DoryErrofbi
Answered 2022-10-24 Author has 12 answers
Note that 25 2 = 625 25 mod 100, so that in fact 25 n 25 mod 100 for any n. Because ϕ ( 100 ) = 40, by Euler's theorem we have that a 40 1 mod 100 for any a relatively prime to 100 (as 23 is). Thus 23 41 23 mod 100. Now put these results together to find
23 41 25 40 mod 100.
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Deborah Proctor
Answered 2022-10-25 Author has 3 answers
On applying   a b mod a c =   a ( b mod c ) = mod Distributive Law we get
25 1 + J 23 1 + 2 K mod 100 = 25 ( 25 J 23 1 + 2 K   1 J ( 1 ) 1 + 2 K   3 mod 4 ) = 25 ( 3 )
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In a box there are 16 ice-creams: 6 lemon flavor,4 mint flavor and 6 strawberry flavor.When we extract two ice-creams,what's the probability of getting two different flavors,given that at least one is strawberry flavor.
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P ( A ) = "Different flavors" = ( 16 2 ) 16 !
P ( B c ) = "At least one is strawberry flavor" = 1 ( 10 2 ) 16 !
We want P ( A | B c ) using conditional probability, where I go wrong?

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