Combinations Questions

The value of ${}^{50}{C}_4+{\sum }_{r=1}^6{}^{56-r}{C}_3$ is:

From $6$ different novels and $3$ different dictionaries, $4$ novels and $1$ dictionary are to be selected and arranged in a row on the shelf so that the dictionary is always in the middle. Then the number of such arrangements is:

The number of ways of distributing $8$ identical balls in $3$ distinct boxes so that none of the boxes is empty is

How many ways are there to arrange the letters in the word GARDEN with the vowels in alphabetical order?