The number of 4 -letter words, with or without meaning, which can be formed using the letters PQRPQRSTUVP, is _ _ _ _ .

Step-by-step solution

Letters: P(3), Q(2), R(2), S(1), T(1), U(1), V(1) — 7 distinct letters. All distinct: 7 4 4! = 840 . One pair + 2 distinct: choose repeating letter from P,Q,R (3 ways), choose 2 from remaining 6 ( 6 2 =15 ), arrange = 4!/2! = 12 . Total = 3 15 12 = 540 . Two pairs: choose 2 from P,Q,R ( 3 2 =3 ), arrange = 4!/(2!2!) = 6 . Total = 18 . One triple + 1 distinct: only P can repeat 3 times, choose 1 from 6, arrange = 4!/3! = 4 . Total = 24 . Answer = 840 + 540 + 18 + 24 = 1422 .