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

Question

Accepted Answer

Correct answer: 1422. (1422) Letters: P (3 ) ,Q (2 ) ,R (2 ) ,S (1 ) ,T (1 ) ,U (1 ) ,V (1 )-7 distinct letters. All distinct: ( 74 ) 4 !=840. One pair +2 distinct: choose repeating letter from P ,Q ,R (3 ways), choose 2 from remaining 6( ( 62 )=15) ), arrange =4 !/2 !=12. Total =3 15 12=540. Two pairs: choose 2 from P ,Q ,R ( ( 32 )=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.

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

Solution

More Permutations & Combinations PYQs