Multinomial Distribution Trouble

#1
I have a homework problem as follows: "You have a deck of 52 cards and take out 35 cards, one-at-a-time with replacement. What is the probability of drawing at least 11 repeated cards?"

To me, this is obviously a multinomial distribution, the basic formula being n!/(n1!*n2! . . .nk!)*(p1^n1*p2^n2 . . .pk^nk). The probability of having 11 or more repeats = (1- the probability of having 10 or fewer) which is a simpler calculation. However, I think I'm doing something wrong. The probality of 0 repeats should be 35!/(1!^35)*(1/52)^35=9.00*10^-21 which seems pretty reasonable. However, it seems logical to me that having exactly 1 repeat should be more likely than 0 repeats, but when I plug in the values to the equation {35!/[2!*(1!^34)]*(1/52)^35} I get 4.50*10^-21. I know that I need to get the probabilites of each possibility from 0 repeats to 10 repeats and sum them together then subtract the sum from 1. Unfortunately, the number I'm getting seems extremely unlikely (as in ~1). I just don't think that the probability of getting 11 or more repeated cards is almost 100%. What am I doing wrong here? Help me understand what step I'm doing wrong so that when I have a similar problem in the future I can solve it without relying on outside help.