Given: The digits \[2,\text{ }3,\text{ }0,\text{ }3,\text{ }4,\text{ }2,\text{ }3\] Total number of digits \[=\text{ }7\] We know, zero cannot be the first digit of the \[7\] digit numbers. Number...

Given: The word \[MADHUBANI\] Total number of letters \[=\text{ }9\] A total number of arrangements of word \[MADHUBANI\] excluding \[I\] Total letters \[8\] Repeating letter \[A\]  repeating twice....

Given: The word \[SERIES\] There are \[6\] letters in the word \[SERIES\] out of which \[2\] are \[Ss,\text{ }2\text{ }are\text{ }Es\] and the rest all are distinct. Now, Let us fix \[5\] letters at...

Given: The digits \[0,\text{ }1,\text{ }1,\text{ }5,\text{ }9\] Total number of digits \[=\text{ }5\] So now, number greater than \[50000\] will have either \[5\text{ }or\text{ }9\] in the first...

There are \[7\] letters in the word \[ARRANGE\]out of which \[2\text{ }are\text{ }As,\text{ }2\text{ }are\text{ }Rs\] and the rest all are distinct. So by using the formula, \[n!/\text{ }\left(...

Given: The digits \[1,\text{ }3,\text{ }3,\text{ }0\] Total number of digits \[=\text{ }4\] Digits of the same type \[=\text{ }2\] Total number of \[4\]digit numbers \[=\text{ }4!\text{ }/\text{...

Given: Number of red flags \[=\text{ }4\] Number of white flags \[=\text{ }2\] Number of green flags \[=\text{ }3\] So there are total \[9\] flags, out of which \[4\] are red, \[2\] are white,...

Given: The digits \[1,\text{ }2,\text{ }3,\text{ }4,\text{ }3,\text{ }2,\text{ }1\] The total number of digits are \[7\] There are \[4\] odd digits \[1,1,3,3\text{ }and\text{ }4\]odd places \[\left(...

Given: The word \[MUMBAI\] There are \[6\] letters in the word \[MUMBAI\]out of which \[2\] are \[Ms\] and the rest all are distinct. So let us consider both \[Ms\]together as one letter, the...

Given: The word \[PARALLEL\] There are \[8\] letters in the word \[PARALLEL\] out of which \[2\text{ }are\text{ }As,\text{ }3\text{ }are\text{ }Ls\] and the rest all are distinct. So by using the...

There are \[9\text{ }\left( i.e\text{ }powers\text{ }3\text{ }+\text{ }2\text{ }+\text{ }4\text{ }=\text{ }9 \right)\]objects in the expression \[{{a}^{3}}~{{b}^{2}}~{{c}^{4}}\] and there are...

Given: The word \[UNIVERSITY\] There are \[10\] letters in the word \[UNIVERSITY\] out of which \[2\text{ }are\text{ }Is\] There are \[4\]vowels in the word \[UNIVERSITY\] out of which \[2\text{...

Given: The word \[ALGEBRA\] There are \[4\]consonants in the word \[ALGEBRA\] The number of ways to arrange these consonants is \[^{4}{{P}_{4}}~=\text{ }4!\] There are \[3\] vowels in the word...

\[CONSTANTINOPLE\] There are \[14\] letters in the word \[CONSTANTINOPLE\]out of which \[2\text{ }are\text{ }Os,\text{ }3\text{ }are\text{ }Ns,\text{ }2\text{ }are\text{ }Ts\]and the rest all are...

(i) \[SERIES\] There are \[6\]letters in the word \[SERIES\]out of which \[2\text{ }are\text{ }Ss,\text{ }2\text{ }are\text{ }Es\]and the rest all are distinct. So by using the formula, \[n!/\text{...

(i) \[PAKISTAN\] There are \[8\]letters in the word \[PAKISTAN\]out of which \[2\text{ }are\text{ }As\]and the rest all are distinct. So by using the formula, \[n!/\text{ }\left( p!\text{ }\times...

(i) \[ARRANGE\] There are \[7\] letters in the word \[ARRANGE\] out of which\[2\text{ }are\text{ }As,\text{ }2\text{ }are\text{ }Rs\] and the rest all are distinct. So by using the formula,...

(i) \[INDEPENDENCE\] There are \[12\] letters in the word \[INDEPENDENCE\] out of which \[2\text{ }are\text{ }Ds,\text{ }3\text{ }are\text{ }Ns,\text{ }4\text{ }are\text{ }Es\]and the rest all are...