(b) 57
He can write 2 or more friends out of 6 friends in the given number of ways:
Invite (i) 2 friends out of 6 friends or
(ii) 3 friends out of 6 friends or
(iii) 4 friends out of 6 friends or
(iv) 5 friends out of 6 friends or
(v) 6 friends out of 6 friends.
∴ Total number of ways of inviting 2 or more friends
= 6C2 + 6C3 + 6C4 + 6C5 + 6C6
= \(\frac{6!}{4!2!}\) + \(\frac{6!}{3!3!}\) + \(\frac{6!}{4!2!}\) + \(\frac{6!}{5!1!}\) + \(\frac{6!}{6!}\)
= \(\frac{6\times5}{2}\) + \(\frac{6\times5\times4}{2}\) + \(\frac{6\times5}{2}\) + 6 + 1
= 15 + 20 + 15 + 6 + 1 = 57.
