JEE MAIN - Mathematics (2020 - 5th September Morning Slot - No. 2)
The number of words, with or without meaning, that can be formed by taking 4 letters at a time from the letters of the word ’SYLLABUS’ such that two letters are distinct and two letters are alike, is :
Answer
240
Explanation
In 'SYLLABUS' word
1. Two S letters
2. Two L letters
3. One Y letter
4. One A letter
5. One B letter
6. One U letter
Number of ways we can select two alike letters = 2C1
Then number of ways we can select two distinct letters = 5C2
Then total arrangement of selected letters = $${{4!} \over {2!}}$$
So total number of words, with or without meaning, that can be formed
= 2C1 $$ \times $$ 5C2 $$ \times $$ $${{4!} \over {2!}}$$ = 240
1. Two S letters
2. Two L letters
3. One Y letter
4. One A letter
5. One B letter
6. One U letter
Number of ways we can select two alike letters = 2C1
Then number of ways we can select two distinct letters = 5C2
Then total arrangement of selected letters = $${{4!} \over {2!}}$$
So total number of words, with or without meaning, that can be formed
= 2C1 $$ \times $$ 5C2 $$ \times $$ $${{4!} \over {2!}}$$ = 240
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