Choose 4 letters from the word ' ARSUN SURESH ' ?
My Approach
A--1
R--2
S--3
U--2
N--1
E--1
H--1 11 letter word .
case 1 : All 4 letters are different
case2 : 2 letters same 2 letters different
case 3 : 2 letters same , 2 letters same
case 4 : 3 letters same , 1 letter different
case 5 : all 4 letters are same
CASE 1
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There are 7 distinct letters and we have to choose 4 from them C(7,4)
CASE 2
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2R's and any 2 distinct OR C(2,2)* C(7,2) +
2S's and any 2 distinct OR C(3,2)* C(7,2) + // Choose two S from three
2U's and any 2 distinct C(2,2)* C(7,2)
CASE 3
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2R's and 2'S C(2,2)* C(3,2) +
2S's and 2U's C(2,2)* C(3,2) +
2U's and 2 R's C(2,2)* C(3,2)
CASE 4
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There are no enough letters . Therefore req no of ways for case4 is 0