In a shop there are five types of ice-creams available. A child buys six ice-creams.
Statement $-1 :$ The number of different ways the child can buy the six ice-creams is $^{10}C_5.$
Statement $-2 :$ The number of different ways the child can buy the six ice-creams is equal to the number of different ways of arranging $6 \,A's$ and $4 \,B's$ in a row.
Statement$-1$ is true, Statement$-2$ is false
Statement $-1$ is true, Statement $-2$ is true; Statement $-2$ is a correct explanation for Statement $-1$
Statement $-1$ is true, Statement $-2$ is true; Statement $-2$ is not acorrect explanation for Statement $-1$
Statement$-1$ is false, Statement$-2$ is true
Six ‘$+$’ and four ‘$-$’ signs are to placed in a straight line so that no two ‘$-$’ signs come together, then the total number of ways are
An urn contains $5$ red marbles, $4$ black marbles and $3$ white marbles. Then the number of ways in which $4$ marbles can be drawn so that at the most three of them are red is
A group consists of $4$ girls and $7$ boys. In how many ways can a team of $5$ members be selected if the team has no girl?
The total number of natural numbers of six digits that can be made with digits $1, 2, 3, 4$, if all digits are to appear in the same number at least once, is
How many words, with or without meaning, can be formed using all the letters of the word $\mathrm{EQUATION}$ at a time so that the vowels and consonants occur together?