Question

# A letter is taken out at random from 'ASSISTANT' and another is taken out from 'STATISTICS'. The probability that they are the same letters is

A
145
B
1290
C
1990
D
None of these

Solution

## The correct option is C $$\cfrac{19}{90}$$In 'ASSISTANT' and 'STATISTICS', the same letters are A,I,S,TProbability of choosing $$\quad A=\cfrac { { _{ }^{ 2 }{ C } }_{ 1 } }{ { _{ }^{ 9 }{ C } }_{ 1 } } \times \cfrac { { _{ }^{ 1 }{ C } }_{ 1 } }{ { _{ }^{ 10 }{ C } }_{ 1 } } =\cfrac { 1 }{ 45 }$$$$I=\cfrac { { _{ }^{ 1 }{ C } }_{ 1 } }{ { _{ }^{ 9 }{ C } }_{ 1 } } \times \cfrac { { _{ }^{ 2 }{ C } }_{ 1 } }{ { _{ }^{ 10 }{ C } }_{ 1 } } =\cfrac { 1 }{ 45 }$$$$S=\cfrac { { _{ }^{ 3 }{ C } }_{ 1 } }{ { _{ }^{ 9 }{ C } }_{ 1 } } \times \cfrac { { _{ }^{ 3 }{ C } }_{ 1 } }{ { _{ }^{ 10 }{ C } }_{ 1 } } =\cfrac { 1 }{ 10 }$$$$T=\cfrac { { _{ }^{ 2 }{ C } }_{ 1 } }{ { _{ }^{ 9 }{ C } }_{ 1 } } \times \cfrac { { _{ }^{ 3 }{ C } }_{ 1 } }{ { _{ }^{ 10 }{ C } }_{ 1 } } =\cfrac { 1 }{ 15 }$$So, total probability$$=\cfrac { 1 }{ 45 } +\cfrac { 1 }{ 45 } +\cfrac { 1 }{ 10 } +\cfrac { 1 }{ 15 } =\cfrac { 19 }{ 90 }$$Maths

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