Six identical coins are arranged in a row. The number of ways in which the number of tails is equal to the number of heads is

The number lock of a suitcase has $4$ wheels,each labelled with ten digits,i.e.,from $0$ to $9$. The lock opens with a sequence of four digits with no repeats. What is the probability of a person getting the right sequence to open the suitcase?

Find $r$ if $^{5}P_{r} = 2 \times ^{6}P_{r-1}$.

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

How many words,with or without meaning,each of $3$ vowels and $2$ consonants can be formed from the letters of the word $INVOLUTE$?

In how many ways can the letters of the word "$ASSASSINATION$" be arranged so that all $S$'s are together?