1. Tardigrade
  2. Question
  3. Mathematics
  4. A child has a set of 26 alphabetized blocks and stacks 10 of these blocks in the shape of a pyramid. The number of possible 10-block pyramids (as shown) that can be formed from the entire set of 26 blocks in an english alphabet is

Question Error Report

Thank you for reporting, we will resolve it shortly

Back to Question

Q. A child has a set of 26 alphabetized blocks and stacks 10 of these blocks in the shape of a pyramid.
The number of possible 10-block pyramids (as shown) that can be formed from the entire set of 26 blocks in an english alphabet isMathematics Question Image

Permutations and Combinations

Solution:

We can arrange the first four blocks in ${ }^{26} P _4$ ways, then the next three blocks in ${ }^{22} P _3$ ways since only 22 blocks remain. Then we can arrange the next two in ${ }^{19} P _2$ ways and the top block can be picked in ${ }^{17} P _1$ ways. Since we are forming a single group (a pyramid) we multiply all the cases together.