Number of ways in which the letters of the word "TOMATO" can be arranged if two alike vowels are separated, is not equal to

Question

Number of ways in which the letters of the word "TOMATO" can be arranged if two alike vowels are separated, is not equal to (A) number of ways in which letters of the word "RAITHATHA" can be arranged if no two alike letters are separated. (B) number of 3 digit numbers with atleast one 3 and atleast one 2. (C) number of ways in which Ram and Rama can exchange their maps if Ram has 3 and Rama has 7 maps, all maps being different, maintaining their original number of maps at the end. (D) number of ways in which 2 alike apples and 4 alike oranges can be distributed in three children if each child get none, one or more fruits.

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Q. Number of ways in which the letters of the word "TOMATO" can be arranged if two alike vowels are separated, is not equal to

number of ways in which letters of the word "RAITHATHA" can be arranged if no two alike letters are separated.

number of 3 digit numbers with atleast one 3 and atleast one 2.

number of ways in which Ram and Rama can exchange their maps if Ram has 3 and Rama has 7 maps, all maps being different, maintaining their original number of maps at the end.

number of ways in which 2 alike apples and 4 alike oranges can be distributed in three children if each child get none, one or more fruits.