The total number of ways of selecting five letters from the letters of the word INDEPENDENT, is

There are 11 letters in the word INDEPENDENT.3N, 3E, 2D, I, P, T (6 types)Different possibilities of choosing 5 letters are(A) All different Number of ways =6C5×5!=6×120=720.(B) 2 alike, 3 differentNumber of ways =3C1×5C3×5!2!=3×10×60=1800(C) 3 alike, 2 differentNumber of ways =2C1×5C2×5!3!= 2 × 10 × 20 = 400(D) 2 alike, 2 alike, 1 different=3C2×4C1×5!2!2!=3×4×30=360(E) 3 alike, 2 alike =2C1×2C1×5!3!2!= 2 × 2 × 10 = 40Hence, total number of ways= 720 + 1800 + 400 + 360 + 40 = 3320.