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We have to form words of 4 letters with the letters of the word MATHEMATICS then which of the following statements are true.

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Number of words with all letters different is 1680

Total number of words is 2436

Total number of such formation is greater than 2436

Number of words in which 2 letters are identical is 800

answer is B, D.

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Detailed Solution

M, A, T $\to$ 2
H, E, I, C, S $\to$ 1

Type	COMBINATION	PERMUTATION
ALL DIFFERENT	$^{8} C_{4}$	$^{8} P_{4} = 1680$
2 SAME 2 DIFFERENT	$^{3} C_{1} \times^{7} C_{2}$	$^{3} C_{1} \times^{7} C_{2} = \frac{4!}{2!} = 756$
2 SAME 2 SAME	$^{3} C_{2}$	$^{3} C_{2} = \frac{4!}{2! 2!} = 18$
TOTAL		2454

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