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6.Permutation and Combination
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$'UNIVERSAL'$ શબ્દના કોઈપણ ત્રણ અક્ષરોથી કેટલા શબ્દો બનાવી શકાય ?
A
$504$
B
$405$
C
$540$
D
$450$
Solution
The total number of $3$ letter words which can be formed $=504$.
We have all the letters of the word $UNIVERSAL$ unique.
Hence they can only be used once.
We have to find a $3$ letter word from it.
For the first letter we have $9$ choices as any letter from the word can be used.
For the second letter we get $8$ choices as any letter except the first can be used.
Similarly for the third we get $7$ choices.
Hence the total number of $3$ letter words which can be formed using the letters of the word UNIVERSAL $=9 \times 8 \times 7=504$
Standard 11
Mathematics
