Acode is formed using four of these letters: a, b, i, k, n, o, and t. (note that the order of the letters in the code matters; for example, abik is a different code from baik. )
the size of the sample space is
a.120 b.360 c.840 d.1680
. the probability that the first three letters of the four-letter code are vowels is
a.1/35 b.1/60 c.1/140 d.101/105

To answer this question, use permutation since the order of the letter matters. There are 7 letters and only 4 are to be used for the code. This  is a permutation of 7 taken 4 (7P4) which is equal to 840. Thus, the sample space is 840.
For the next questions, there are 3 vowels for as the first letter, only 6 letters are available for the second, 5 on the next, and 4 on the last. Multiplying these numbers give 360. To solve for probability, divide this number with the sample space. Thus, the answer is 3/7. 

What is the diagram u didn't post that

What’s the question?