In how many different ways can the 9 letters of the word TELESCOPE be arranged so that there are exactly two letters between the $$$\mathrm{T}$$$ and the $$$\mathrm{C}$$$ ? .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... ....................................................................................................................................................

Mathematics

IGCSE&ALevel

CAIE

Exam No：9709_w21_qp_52 Year：2021 Question No：4(b)

Answer:

$\frac{7 !}{3 !} \times 2 \times 6$
10080
Alternative method for question
$\frac{{ }^{7} \mathrm{P}_{2} \times 6 ! \times 2}{3 !}$
10080
Alternative method for question
$\frac{7 !}{3 !} \times 4 \mathrm{P} 2$
10080

Knowledge points:

5.2.2.1 repetition (e.g. the number of ways of arranging the letters of the word ‘NEEDLESS’)

5.2.2.2 restriction (e.g. the number of ways several people can stand in a line if two particular people must, or must not, stand next to each other). (Questions may include cases such as people sitting in two (or more) rows.) (Questions about objects arranged in a circle will not be included.)

Answer:

Knowledge points:

Solution:

Related Question