Yusuf's Brothers ask Ya`qub's Permission to send Their Brother Binyamin with Them to Egypt

Allah says that when they went back to their father,

قَالُواْ يأَبَانَا مُنِعَ مِنَّا الْكَيْلُ

Therefore, he said: فَاللَّـهُ خَيْرٌ‌ حَافِظًا (Well, Allah is the best guardian - 64), that is, he had already seen the outcome of their guardianship earlier, now he was placing his trust in Allah Ta` ala alone as his guardian. Then, he added: وَهُوَ أَرْ‌حَمُ الرَّ‌احِمِينَ (and He is the most merciful of all the merciful - 64), that is, only from Him, he could hope that He would look at his old age and the sorrows he was surrounded with and would not let more shocks shake him.

In short, Sayyidna Ya` qub (علیہ السلام) did not rely on apparent conditions and on the pledges given by his sons, but did agree to send his youngest son with his brothers solely because he had now placed his trust in Allah Ta` ala.