The total number of injections (one-one into mappings) from a1,a2,a3,a4 to b1,b2,b3,b4,b5,b6,b7 is
400
420
800
840
One one into mappings:
Given : A=a1,a2,a3,a4 and B=b1,b2,b3,b4,b5,b6,b7
n(A)=4 and n(B)=7
Therefore, total number of injections=P47
=7!3!=7×6×5×4×3!3!=840
Hence option (D) is the correct option.
Let A={a1,a2,a3,a4,a5} and B={b1,b2,b3,b4,b5} where ai's and bi's are school going students . Define a relation from A to B by xRy iff y is a true friend of x . If R={(a1,b1),(a2,b2),(a3,b3),(a4,b4),(a5,b5)} . Prove that R is neither one one nor onto