Many new guitarists have such a problem with the Fmajor chord because it involves a new concept; using your first finger to press down frets on two strings.
Start by placing your first finger on the first frets of both the first and second strings. Now, slightly roll the finger back (towards the headstock of the guitar). Many people find this technique makes playing the Fmajor chord slightly easier. Next, place your second finger on the second fret of the third string. Lastly, place your third finger on the third fret of the fourth string. Strum only the bottom four strings, and you're playing an Fmajor chord.
Chances are, at first, very few, if any of the notes will ring when trying to strum this chord. Check to make sure your second and third fingers are curled, and not flattened against the other strings of the guitar. Although this chord seems nearly impossible at first, within weeks, you'll have it sounding as good as the rest of the chords you play.