The letters of word "RADHIKA" are permuted and arranged in alphabetical order as in English dictionary. The number of words the appear before the word "RADHIKA" is

Question

The letters of word "RADHIKA" are permuted and arranged in alphabetical order as in English dictionary. The number of words the appear before the word "RADHIKA" is (A) 2193 (B) 2195 (C) 2119 (D) 2192

Tardigrade Admin · Accepted Answer

Words starting form A=6 !=720 words starting from D, H, I, K=(6 !/2 !) × 4=1440 Word starting form RAA =4 !=24 RADA=3 !=6 RADHA =2 !=2 RADHIAK =1 Thus, number of words before RADHIKA = 2193

Q. The letters of word "RADHIKA" are permuted and arranged in alphabetical order as in English dictionary. The number of words the appear before the word "RADHIKA" is

2193

2195

2119

2192

Words starting form $A = 6! = 720$
words starting from $D, H, I, K = \frac{6 !}{2 !} \times 4 = 1440$
Word starting form $R AA = 4! = 24$
RADA $= 3! = 6$
RADHA $= 2! = 2$
RADHIAK $= 1$
Thus, number of words before RADHIKA $= 2193$

Q. The letters of word "RADHIKA" are permuted and arranged in alphabetical order as in English dictionary. The number of words the appear before the word "RADHIKA" is

2193

2195

2119

2192

Words starting form A=6!=720 words starting from D,H,I,K=2!6!​×4=1440 Word starting form RAA=4!=24 RADA=3!=6 RADHA =2!=2 RADHIAK =1 Thus, number of words before RADHIKA =2193

Words starting form $A = 6! = 720$
words starting from $D, H, I, K = \frac{6 !}{2 !} \times 4 = 1440$
Word starting form $R AA = 4! = 24$
RADA $= 3! = 6$
RADHA $= 2! = 2$
RADHIAK $= 1$
Thus, number of words before RADHIKA $= 2193$