How easily can I lose 10 pounds?

I'm a female, I weigh 106 pounds, and I'm 5'0 tall. I plan on only eating fruits and vegetables, grilled chicken breast, and beans and such for protein. I'm going to run every other day, and do pilates. I'm going to change my caloric intake everyday. So, like, one day i'll eat 1,200. The next I'll eat 1,500. Will it be possible to lose 10 pounds by June 23rd? What else do you suggest?