Question

Consider the following statements
Statement I The number of ways a lawn tennis mixed double be made up from seven married couples, if no husband and wife play in the same set are 840.
Statement II The number of words beginning with $T$ and ending with $E$ on arranging letters of the word 'TRIANGLE' are 720.
Choose the correct option.

• A. Only Statement I is correct
• B. Only Statement II is correct
• C. Both I and II are correct
• D. Neither I nor II is correct

Answer 1

Answer: (C)

I. We have seven married couples.
$\therefore$ Two husbands can be selected in $7\times 6=42$ ways.
Two wives can be selected in $5\times 4=20$ ways.
(as wives of husband's selected cannot play in same set)
$\therefore$ Required number of ways $=42\times 20=840$
II. The number of words beginning with $T$ and ending with $E$
$=6\text{ ! }$
( rest 6 alphabets can be arranged in $6!$ ways) $=720$ ways