Is there a significance to 50 days between Easter and Pentecost?

Pentecost means “the fiftieth day” and was originally a Jewish festival of the first-fruits of the harvest, a part of the Festival of Weeks. The Festival of Weeks, also known as Shavuot, is a Jewish holiday celebrated seven weeks after Passover, commemorating the first fruits of the harvest and the giving of the Torah on Mount Sinai. It’s a pilgrimage festival, which meant that Jewish people from many nations would be present. After the events of Acts 1:1-21, Christians decided to keep the name “Pentecost” because of it being 50 days after Easter. There’s also a connection to the first-fruits as, on the first Pentecost, there was a gathering of around 3,000 who were given new life by the Holy Spirit.

Why are women specifically mentioned in Jesus' genealogy?

Five women are mentioned in Matthew’s genealogy of Jesus: Tamar, Rahab, Ruth, Bathsheba, and Mary. The Rev Timothy Appel explains the inclusion of these women well on an episode of “Sharper Iron” from KFUO radio:

“The first and fourth women involve particularly scandalous events from all parties involved; the second and third women are Gentiles who are included in the people of God. Each one shows God’s faithfulness to bring the Savior into the world, which He accomplishes through the most unlikely woman of all: the Virgin Mary. Each name mentioned points us to Jesus, the Savior whose birth Matthew is about to proclaim.”