The number of words of 4 letters which can be formed with the letters of the word MATHEMATICS is α, then (α)/300 is

Question

MARKS Content Team · Accepted Answer

Correct answer: 8.18. M,A,T→2 H,E,I,C,S→1 Type Combination Permutation all different ^8C_4 ^8P_4=1680 2 same 2 different ^3C_1×^7C_1 ^3C_1×^7C_1×(4!)/(2!)=756 2 same 2 same ^3C_2 ^3C_2×(4!)/(2!)=18 Total number of words =2454 2454/300=8.18

The number of words of $4$ letters which can be formed with the letters of the word $M A T H E M A T I C S$ is $α$ , then $\frac{α}{300}$ is

Solution

More Permutation Combination Questions

Type	Combination	Permutation
all different	$^{8} C_{4}$	$^{8} P_{4} = 1680$
2 same 2 different	$^{3} C_{1} \times^{7} C_{1}$	$^{3} C_{1} \times^{7} C_{1} \times \frac{4!}{2!} = 756$
2 same 2 same	$^{3} C_{2}$	$^{3} C_{2} \times \frac{4!}{2!} = 18$

The number of words of 4 letters which can be formed with the letters of the word MATHEMATICS is α, then α300 is

Solution

More Permutation Combination Questions

The number of words of $4$ letters which can be formed with the letters of the word $M A T H E M A T I C S$ is $α$ , then $\frac{α}{300}$ is