Question

7. In a group photograph, 6 teachers are in the first row and 18 students are in the second row. There are 12 boys and 6 girls among the students. If the middle position is reserved for the principal and if no two girls are together, find the number of arrangements.

8. Find the number of ways so that letters of
the word HISTORY can be arranged as,
(a) Y and T are together
(b) Y is next to T.
(c) there is no restriction
(d) begin and end with vowel
(e) end in ST
(f) begin with S and end with T ​

Answer 1

Word HISTORY can be arranged  in 5040 ways if no restriction

Step-by-step explanation:

word HISTORY

has 7 Letters

(a) Y and T are together

YT together as 1  - can be arranged in 2 ways

remaining 5 + YT as 1 = 6

so 6! * 2 = 1440 Ways

(b) Y is next to T.

Same case as above but TY is not includes

Hence 1440/2 = 720 Ways

(c) there is no restriction

= 7!

= 5040 Ways

(d) begin and end with vowel

2 * 5!  = 240  Ways

(e) end in ST

= 5!  

= 120 Ways

(f) begin with S and end with T ​

= 5!

= 120 Ways

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