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

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

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

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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