whats the mumber of injections f from S={1,2,3,4,5} to T={a,b,c,d,e,f} such that f(1)!=a and f(2)=!b ?   i came to the conclusion 5^2 x 4^2 x 3 because:   f(1) has 5 ways (when we exclude a and b) (2) has 4 (excluding a,b, f(1)) f(3) is back to 5 ( excluding f(1), f(2), but putting back a and b) f(4) has 4 f(5) has 3

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter6: The Trigonometric Functions
Section6.4: Values Of The Trigonometric Functions
Problem 21E
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whats the mumber of injections f from S={1,2,3,4,5} to T={a,b,c,d,e,f} such that f(1)!=a and f(2)=!b ?

 

i came to the conclusion 5^2 x 4^2 x 3 because:

 

f(1) has 5 ways (when we exclude a and b)

(2) has 4 (excluding a,b, f(1))

f(3) is back to 5 ( excluding f(1), f(2), but putting back a and b)

f(4) has 4

f(5) has 3

 

is this correct?

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